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

Percentage Accurate: 98.5% → 98.5%

Time: 19.0s

Alternatives: 25

Speedup: 1.0×

• 47.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Final simplification 97.6%

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

Alternative 2: 88.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -3.6e+196)
     t_1
     (if (<= y 1.8e+67) (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -3.6e+196) {
		tmp = t_1;
	} else if (y <= 1.8e+67) {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * (z ** y)) / a) / y
    if (y <= (-3.6d+196)) then
        tmp = t_1
    else if (y <= 1.8d+67) then
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -3.6e+196) {
		tmp = t_1;
	} else if (y <= 1.8e+67) {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -3.6e+196:
		tmp = t_1
	elif y <= 1.8e+67:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -3.6e+196)
		tmp = t_1;
	elseif (y <= 1.8e+67)
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -3.6e+196)
		tmp = t_1;
	elseif (y <= 1.8e+67)
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3.6e+196], t$95$1, If[LessEqual[y, 1.8e+67], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.60000000000000007e196 or 1.7999999999999999e67 < 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. Step-by-step derivation

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. exp-diff N/A

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

      4. prod-exp N/A

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

      5. *-commutative N/A

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

      6. pow-to-exp N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. pow-to-exp N/A

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

      11. clear-num N/A

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

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

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

   4. Applied egg-rr 50.0%

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

   5. Taylor expanded in t around 0

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

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

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

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

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

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

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

      4. exp-lowering-exp.f64 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in b around 0

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

      1. associate-/r* N/A

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

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

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

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

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

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

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

      5. pow-lowering-pow.f64 93.7%

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

   10. Simplified 93.7%

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

   if -3.60000000000000007e196 < y < 1.7999999999999999e67

   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

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 93.1%

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

   5. Simplified 93.1%

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

Alternative 3: 80.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 11:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}} \cdot {a}^{t}}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -2.2e+106)
     t_1
     (if (<= y 11.0) (/ (* (/ x (* y (exp b))) (pow a t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -2.2e+106) {
		tmp = t_1;
	} else if (y <= 11.0) {
		tmp = ((x / (y * exp(b))) * pow(a, t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * (z ** y)) / a) / y
    if (y <= (-2.2d+106)) then
        tmp = t_1
    else if (y <= 11.0d0) then
        tmp = ((x / (y * exp(b))) * (a ** t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -2.2e+106) {
		tmp = t_1;
	} else if (y <= 11.0) {
		tmp = ((x / (y * Math.exp(b))) * Math.pow(a, t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -2.2e+106:
		tmp = t_1
	elif y <= 11.0:
		tmp = ((x / (y * math.exp(b))) * math.pow(a, t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -2.2e+106)
		tmp = t_1;
	elseif (y <= 11.0)
		tmp = Float64(Float64(Float64(x / Float64(y * exp(b))) * (a ^ t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -2.2e+106)
		tmp = t_1;
	elseif (y <= 11.0)
		tmp = ((x / (y * exp(b))) * (a ^ t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2.2e+106], t$95$1, If[LessEqual[y, 11.0], N[(N[(N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.19999999999999992e106 or 11 < 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. Step-by-step derivation

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. exp-diff N/A

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

      4. prod-exp N/A

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

      5. *-commutative N/A

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

      6. pow-to-exp N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. pow-to-exp N/A

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

      11. clear-num N/A

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

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

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

   4. Applied egg-rr 47.1%

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

   5. Taylor expanded in t around 0

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

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

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

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

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

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

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

      4. exp-lowering-exp.f64 58.9%

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

   7. Simplified 58.9%

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

   8. Taylor expanded in b around 0

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

      1. associate-/r* N/A

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

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

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

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

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

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

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

      5. pow-lowering-pow.f64 86.5%

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

   10. Simplified 86.5%

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

   if -2.19999999999999992e106 < y < 11

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 94.6%

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

   5. Simplified 94.6%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. pow-to-exp N/A

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

      4. clear-num N/A

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

      5. div-inv N/A

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

      6. associate-/r/ N/A

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

      7. unpow-prod-up N/A

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

      8. associate-*r* N/A

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

      9. unpow-1 N/A

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

      10. un-div-inv N/A

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

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

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

   7. Applied egg-rr 87.6%

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

Alternative 4: 57.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-260}:\\ \;\;\;\;\frac{\frac{1}{y}}{\frac{\frac{\frac{-18}{x} - \frac{\frac{18}{x} + \frac{-18}{x \cdot b}}{b}}{b} - \frac{6}{x}}{b \cdot \left(b \cdot b\right)}}\\ \mathbf{elif}\;b \leq 29000:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -3.3e+14)
     t_1
     (if (<= b 4.6e-260)
       (/
        (/ 1.0 y)
        (/
         (-
          (/ (- (/ -18.0 x) (/ (+ (/ 18.0 x) (/ -18.0 (* x b))) b)) b)
          (/ 6.0 x))
         (* b (* b b))))
       (if (<= b 29000.0) (/ (/ x y) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double tmp;
	if (b <= -3.3e+14) {
		tmp = t_1;
	} else if (b <= 4.6e-260) {
		tmp = (1.0 / y) / (((((-18.0 / x) - (((18.0 / x) + (-18.0 / (x * b))) / b)) / b) - (6.0 / x)) / (b * (b * b)));
	} else if (b <= 29000.0) {
		tmp = (x / y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / exp(b)) / y
    if (b <= (-3.3d+14)) then
        tmp = t_1
    else if (b <= 4.6d-260) then
        tmp = (1.0d0 / y) / ((((((-18.0d0) / x) - (((18.0d0 / x) + ((-18.0d0) / (x * b))) / b)) / b) - (6.0d0 / x)) / (b * (b * b)))
    else if (b <= 29000.0d0) then
        tmp = (x / y) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / Math.exp(b)) / y;
	double tmp;
	if (b <= -3.3e+14) {
		tmp = t_1;
	} else if (b <= 4.6e-260) {
		tmp = (1.0 / y) / (((((-18.0 / x) - (((18.0 / x) + (-18.0 / (x * b))) / b)) / b) - (6.0 / x)) / (b * (b * b)));
	} else if (b <= 29000.0) {
		tmp = (x / y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -3.3e+14:
		tmp = t_1
	elif b <= 4.6e-260:
		tmp = (1.0 / y) / (((((-18.0 / x) - (((18.0 / x) + (-18.0 / (x * b))) / b)) / b) - (6.0 / x)) / (b * (b * b)))
	elif b <= 29000.0:
		tmp = (x / y) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -3.3e+14)
		tmp = t_1;
	elseif (b <= 4.6e-260)
		tmp = Float64(Float64(1.0 / y) / Float64(Float64(Float64(Float64(Float64(-18.0 / x) - Float64(Float64(Float64(18.0 / x) + Float64(-18.0 / Float64(x * b))) / b)) / b) - Float64(6.0 / x)) / Float64(b * Float64(b * b))));
	elseif (b <= 29000.0)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -3.3e+14)
		tmp = t_1;
	elseif (b <= 4.6e-260)
		tmp = (1.0 / y) / (((((-18.0 / x) - (((18.0 / x) + (-18.0 / (x * b))) / b)) / b) - (6.0 / x)) / (b * (b * b)));
	elseif (b <= 29000.0)
		tmp = (x / y) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -3.3e+14], t$95$1, If[LessEqual[b, 4.6e-260], N[(N[(1.0 / y), $MachinePrecision] / N[(N[(N[(N[(N[(-18.0 / x), $MachinePrecision] - N[(N[(N[(18.0 / x), $MachinePrecision] + N[(-18.0 / N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - N[(6.0 / x), $MachinePrecision]), $MachinePrecision] / N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 29000.0], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.3e14 or 29000 < 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. exp-neg N/A

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

      4. 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 -3.3e14 < b < 4.6e-260

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 20.6%

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

   5. Simplified 20.6%

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

   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 20.6%

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

   8. Simplified 20.6%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{x + b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{y} \cdot \color{blue}{\left(x + b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)} \]

      3. flip3-+ N/A

         \[\leadsto \frac{1}{y} \cdot \frac{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}{\color{blue}{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{y} \cdot \frac{1}{\color{blue}{\frac{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}}} \]

      5. un-div-inv N/A

         \[\leadsto \frac{\frac{1}{y}}{\color{blue}{\frac{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{y}\right), \color{blue}{\left(\frac{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}\right)}\right) \]

   10. Applied egg-rr 20.6%

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

   11. Taylor expanded in b around -inf

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{18 \cdot \frac{1}{x} - 18 \cdot \frac{1}{b \cdot x}}{b} - 18 \cdot \frac{1}{x}}{b} + 6 \cdot \frac{1}{x}}{{b}^{3}}\right)}\right) \]

   13. Simplified 43.4%

       \[\leadsto \frac{\frac{1}{y}}{\color{blue}{\frac{\frac{6}{x} - \frac{\frac{\frac{18}{x} + \frac{-18}{x \cdot b}}{0 - b} + \frac{-18}{x}}{b}}{-b \cdot \left(b \cdot b\right)}}} \]

   if 4.6e-260 < b < 29000

   1. Initial program 92.1%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in b around 0

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

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

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

      2. exp-to-pow N/A

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 74.0%

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

   8. Simplified 74.0%

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

   9. Taylor expanded in t around 0

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

       1. *-commutative N/A

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

       2. associate-/r* N/A

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

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

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

       4. /-lowering-/.f64 50.6%

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

   11. Simplified 50.6%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-260}:\\ \;\;\;\;\frac{\frac{1}{y}}{\frac{\frac{\frac{-18}{x} - \frac{\frac{18}{x} + \frac{-18}{x \cdot b}}{b}}{b} - \frac{6}{x}}{b \cdot \left(b \cdot b\right)}}\\ \mathbf{elif}\;b \leq 29000:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -2.7e+196)
     t_1
     (if (<= y 4.2e+65) (/ x (* y (* a (exp b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -2.7e+196) {
		tmp = t_1;
	} else if (y <= 4.2e+65) {
		tmp = x / (y * (a * exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * (z ** y)) / a) / y
    if (y <= (-2.7d+196)) then
        tmp = t_1
    else if (y <= 4.2d+65) then
        tmp = x / (y * (a * exp(b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -2.7e+196) {
		tmp = t_1;
	} else if (y <= 4.2e+65) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -2.7e+196:
		tmp = t_1
	elif y <= 4.2e+65:
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -2.7e+196)
		tmp = t_1;
	elseif (y <= 4.2e+65)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -2.7e+196)
		tmp = t_1;
	elseif (y <= 4.2e+65)
		tmp = x / (y * (a * exp(b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2.7e+196], t$95$1, If[LessEqual[y, 4.2e+65], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.69999999999999995e196 or 4.19999999999999983e65 < 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. Step-by-step derivation

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. exp-diff N/A

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

      4. prod-exp N/A

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

      5. *-commutative N/A

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

      6. pow-to-exp N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. pow-to-exp N/A

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

      11. clear-num N/A

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

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

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

   4. Applied egg-rr 50.0%

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

   5. Taylor expanded in t around 0

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

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

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

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

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

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

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

      4. exp-lowering-exp.f64 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in b around 0

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

      1. associate-/r* N/A

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

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

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

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

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

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

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

      5. pow-lowering-pow.f64 93.7%

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

   10. Simplified 93.7%

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

   if -2.69999999999999995e196 < y < 4.19999999999999983e65

   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

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 93.1%

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

   5. Simplified 93.1%

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

      1. exp-diff N/A

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

      2. pow-to-exp N/A

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

      3. unpow-prod-up N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

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

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

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

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

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

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

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

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

      10. unpow-1 N/A

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

      11. metadata-eval N/A

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

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

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

      13. metadata-eval N/A

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

      14. exp-lowering-exp.f64 84.3%

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

   7. Applied egg-rr 84.3%

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

   8. Taylor expanded in t around 0

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

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

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

      7. exp-lowering-exp.f64 76.4%

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

   10. Simplified 76.4%

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

Alternative 6: 76.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 72000000:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -4.2e+14)
     t_1
     (if (<= b 72000000.0) (/ (* x (pow a (+ t -1.0))) 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 <= -4.2e+14) {
		tmp = t_1;
	} else if (b <= 72000000.0) {
		tmp = (x * pow(a, (t + -1.0))) / 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 <= (-4.2d+14)) then
        tmp = t_1
    else if (b <= 72000000.0d0) then
        tmp = (x * (a ** (t + (-1.0d0)))) / 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 <= -4.2e+14) {
		tmp = t_1;
	} else if (b <= 72000000.0) {
		tmp = (x * Math.pow(a, (t + -1.0))) / 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 <= -4.2e+14:
		tmp = t_1
	elif b <= 72000000.0:
		tmp = (x * math.pow(a, (t + -1.0))) / 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 <= -4.2e+14)
		tmp = t_1;
	elseif (b <= 72000000.0)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / 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 <= -4.2e+14)
		tmp = t_1;
	elseif (b <= 72000000.0)
		tmp = (x * (a ^ (t + -1.0))) / 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, -4.2e+14], t$95$1, If[LessEqual[b, 72000000.0], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.2e14 or 7.2e7 < 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. exp-neg N/A

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

      4. 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 -4.2e14 < b < 7.2e7

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in b around 0

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

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

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

      2. exp-to-pow N/A

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 71.7%

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

   8. Simplified 71.7%

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

Alternative 7: 74.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -6 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 31000:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -6e+14)
     t_1
     (if (<= b 31000.0) (* (pow a (+ t -1.0)) (/ x 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 <= -6e+14) {
		tmp = t_1;
	} else if (b <= 31000.0) {
		tmp = pow(a, (t + -1.0)) * (x / 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 <= (-6d+14)) then
        tmp = t_1
    else if (b <= 31000.0d0) then
        tmp = (a ** (t + (-1.0d0))) * (x / 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 <= -6e+14) {
		tmp = t_1;
	} else if (b <= 31000.0) {
		tmp = Math.pow(a, (t + -1.0)) * (x / 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 <= -6e+14:
		tmp = t_1
	elif b <= 31000.0:
		tmp = math.pow(a, (t + -1.0)) * (x / 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 <= -6e+14)
		tmp = t_1;
	elseif (b <= 31000.0)
		tmp = Float64((a ^ Float64(t + -1.0)) * Float64(x / 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 <= -6e+14)
		tmp = t_1;
	elseif (b <= 31000.0)
		tmp = (a ^ (t + -1.0)) * (x / 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, -6e+14], t$95$1, If[LessEqual[b, 31000.0], N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6e14 or 31000 < 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. exp-neg N/A

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

      4. 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 -6e14 < b < 31000

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. exp-to-pow N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

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

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

      9. /-lowering-/.f64 69.5%

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

   8. Simplified 69.5%

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

Alternative 8: 67.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \frac{{z}^{y}}{a}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ x y) (/ (pow z y) a))))
   (if (<= y -4.2e+215)
     t_1
     (if (<= y 2.4e+65) (/ x (* y (* a (exp b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) * (pow(z, y) / a);
	double tmp;
	if (y <= -4.2e+215) {
		tmp = t_1;
	} else if (y <= 2.4e+65) {
		tmp = x / (y * (a * exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) * ((z ** y) / a)
    if (y <= (-4.2d+215)) then
        tmp = t_1
    else if (y <= 2.4d+65) then
        tmp = x / (y * (a * exp(b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) * (Math.pow(z, y) / a);
	double tmp;
	if (y <= -4.2e+215) {
		tmp = t_1;
	} else if (y <= 2.4e+65) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / y) * (math.pow(z, y) / a)
	tmp = 0
	if y <= -4.2e+215:
		tmp = t_1
	elif y <= 2.4e+65:
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / y) * Float64((z ^ y) / a))
	tmp = 0.0
	if (y <= -4.2e+215)
		tmp = t_1;
	elseif (y <= 2.4e+65)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / y) * ((z ^ y) / a);
	tmp = 0.0;
	if (y <= -4.2e+215)
		tmp = t_1;
	elseif (y <= 2.4e+65)
		tmp = x / (y * (a * exp(b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+215], t$95$1, If[LessEqual[y, 2.4e+65], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2000000000000003e215 or 2.4000000000000002e65 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

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

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

      9. exp-to-pow N/A

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

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

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

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

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

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

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

      15. /-lowering-/.f64 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in t around 0

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

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

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

      2. pow-lowering-pow.f64 79.0%

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

   8. Simplified 79.0%

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

   if -4.2000000000000003e215 < y < 2.4000000000000002e65

   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

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 92.6%

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

   5. Simplified 92.6%

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

      1. exp-diff N/A

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

      2. pow-to-exp N/A

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

      3. unpow-prod-up N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

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

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

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

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

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

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

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

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

      10. unpow-1 N/A

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

      11. metadata-eval N/A

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

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

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

      13. metadata-eval N/A

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

      14. exp-lowering-exp.f64 83.9%

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

   7. Applied egg-rr 83.9%

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

   8. Taylor expanded in t around 0

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

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

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

      7. exp-lowering-exp.f64 76.1%

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

   10. Simplified 76.1%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+215}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{z}^{y}}{a}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{z}^{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{t}}{y}\\ \mathbf{if}\;t \leq -35000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a t)) y)))
   (if (<= t -35000000.0) t_1 (if (<= t 6.2) (/ x (* y (* a (exp b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, t)) / y;
	double tmp;
	if (t <= -35000000.0) {
		tmp = t_1;
	} else if (t <= 6.2) {
		tmp = x / (y * (a * exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (a ** t)) / y
    if (t <= (-35000000.0d0)) then
        tmp = t_1
    else if (t <= 6.2d0) then
        tmp = x / (y * (a * exp(b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, t)) / y;
	double tmp;
	if (t <= -35000000.0) {
		tmp = t_1;
	} else if (t <= 6.2) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, t)) / y
	tmp = 0
	if t <= -35000000.0:
		tmp = t_1
	elif t <= 6.2:
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ t)) / y)
	tmp = 0.0
	if (t <= -35000000.0)
		tmp = t_1;
	elseif (t <= 6.2)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ t)) / y;
	tmp = 0.0;
	if (t <= -35000000.0)
		tmp = t_1;
	elseif (t <= 6.2)
		tmp = x / (y * (a * exp(b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -35000000.0], t$95$1, If[LessEqual[t, 6.2], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5e7 or 6.20000000000000018 < 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 y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in b around 0

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

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

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

      2. exp-to-pow N/A

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 76.7%

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

   8. Simplified 76.7%

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

   9. Taylor expanded in t around inf

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

   11. Simplified 76.7%

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

   if -3.5e7 < t < 6.20000000000000018

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 72.8%

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

   5. Simplified 72.8%

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

      1. exp-diff N/A

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

      2. pow-to-exp N/A

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

      3. unpow-prod-up N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

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

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

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

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

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

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

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

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

      10. unpow-1 N/A

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

      11. metadata-eval N/A

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

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

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

      13. metadata-eval N/A

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

      14. exp-lowering-exp.f64 73.0%

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

   7. Applied egg-rr 73.0%

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

   8. Taylor expanded in t around 0

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

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

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

      7. exp-lowering-exp.f64 73.1%

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

   10. Simplified 73.1%

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

Alternative 10: 65.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-36}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -1e+15) t_1 (if (<= b 1.65e-36) (/ (* 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 <= -1e+15) {
		tmp = t_1;
	} else if (b <= 1.65e-36) {
		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 <= (-1d+15)) then
        tmp = t_1
    else if (b <= 1.65d-36) 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 <= -1e+15) {
		tmp = t_1;
	} else if (b <= 1.65e-36) {
		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 <= -1e+15:
		tmp = t_1
	elif b <= 1.65e-36:
		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 <= -1e+15)
		tmp = t_1;
	elseif (b <= 1.65e-36)
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -1e+15)
		tmp = t_1;
	elseif (b <= 1.65e-36)
		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, -1e+15], t$95$1, If[LessEqual[b, 1.65e-36], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1e15 or 1.64999999999999995e-36 < 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. exp-neg N/A

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

      4. 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%

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

   if -1e15 < b < 1.64999999999999995e-36

   1. Initial program 95.0%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in b around 0

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

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

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

      2. exp-to-pow N/A

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 71.6%

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

   8. Simplified 71.6%

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

   9. Taylor expanded in t around inf

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

   11. Simplified 53.2%

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

Alternative 11: 51.6% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(b \cdot b\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{-133}:\\ \;\;\;\;\frac{\frac{1}{y}}{\frac{\frac{18}{b \cdot t\_1} - \left(\frac{6}{x} + \left(\frac{18}{x \cdot b} + \frac{18}{t\_1}\right)\right)}{b \cdot \left(b \cdot b\right)}}\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-238}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-255}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 105000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* b b))))
   (if (<= b -8.2e-133)
     (/
      (/ 1.0 y)
      (/
       (- (/ 18.0 (* b t_1)) (+ (/ 6.0 x) (+ (/ 18.0 (* x b)) (/ 18.0 t_1))))
       (* b (* b b))))
     (if (<= b -2.6e-238)
       (/ (/ x a) y)
       (if (<= b 6.6e-255)
         (/ (* x (* b (* b 0.5))) y)
         (if (<= b 105000000000.0)
           (/ (/ x y) a)
           (/
            (/
             1.0
             (/
              (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))
              x))
            y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (b * b);
	double tmp;
	if (b <= -8.2e-133) {
		tmp = (1.0 / y) / (((18.0 / (b * t_1)) - ((6.0 / x) + ((18.0 / (x * b)) + (18.0 / t_1)))) / (b * (b * b)));
	} else if (b <= -2.6e-238) {
		tmp = (x / a) / y;
	} else if (b <= 6.6e-255) {
		tmp = (x * (b * (b * 0.5))) / y;
	} else if (b <= 105000000000.0) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))) / x)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (b * b)
    if (b <= (-8.2d-133)) then
        tmp = (1.0d0 / y) / (((18.0d0 / (b * t_1)) - ((6.0d0 / x) + ((18.0d0 / (x * b)) + (18.0d0 / t_1)))) / (b * (b * b)))
    else if (b <= (-2.6d-238)) then
        tmp = (x / a) / y
    else if (b <= 6.6d-255) then
        tmp = (x * (b * (b * 0.5d0))) / y
    else if (b <= 105000000000.0d0) then
        tmp = (x / y) / a
    else
        tmp = (1.0d0 / ((1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0)))))) / x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (b * b);
	double tmp;
	if (b <= -8.2e-133) {
		tmp = (1.0 / y) / (((18.0 / (b * t_1)) - ((6.0 / x) + ((18.0 / (x * b)) + (18.0 / t_1)))) / (b * (b * b)));
	} else if (b <= -2.6e-238) {
		tmp = (x / a) / y;
	} else if (b <= 6.6e-255) {
		tmp = (x * (b * (b * 0.5))) / y;
	} else if (b <= 105000000000.0) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))) / x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (b * b)
	tmp = 0
	if b <= -8.2e-133:
		tmp = (1.0 / y) / (((18.0 / (b * t_1)) - ((6.0 / x) + ((18.0 / (x * b)) + (18.0 / t_1)))) / (b * (b * b)))
	elif b <= -2.6e-238:
		tmp = (x / a) / y
	elif b <= 6.6e-255:
		tmp = (x * (b * (b * 0.5))) / y
	elif b <= 105000000000.0:
		tmp = (x / y) / a
	else:
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))) / x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(b * b))
	tmp = 0.0
	if (b <= -8.2e-133)
		tmp = Float64(Float64(1.0 / y) / Float64(Float64(Float64(18.0 / Float64(b * t_1)) - Float64(Float64(6.0 / x) + Float64(Float64(18.0 / Float64(x * b)) + Float64(18.0 / t_1)))) / Float64(b * Float64(b * b))));
	elseif (b <= -2.6e-238)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 6.6e-255)
		tmp = Float64(Float64(x * Float64(b * Float64(b * 0.5))) / y);
	elseif (b <= 105000000000.0)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))) / x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (b * b);
	tmp = 0.0;
	if (b <= -8.2e-133)
		tmp = (1.0 / y) / (((18.0 / (b * t_1)) - ((6.0 / x) + ((18.0 / (x * b)) + (18.0 / t_1)))) / (b * (b * b)));
	elseif (b <= -2.6e-238)
		tmp = (x / a) / y;
	elseif (b <= 6.6e-255)
		tmp = (x * (b * (b * 0.5))) / y;
	elseif (b <= 105000000000.0)
		tmp = (x / y) / a;
	else
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))) / x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e-133], N[(N[(1.0 / y), $MachinePrecision] / N[(N[(N[(18.0 / N[(b * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(6.0 / x), $MachinePrecision] + N[(N[(18.0 / N[(x * b), $MachinePrecision]), $MachinePrecision] + N[(18.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.6e-238], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6.6e-255], N[(N[(x * N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 105000000000.0], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(1.0 / N[(N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -8.20000000000000045e-133

   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 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 67.9%

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

   5. Simplified 67.9%

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

   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 59.6%

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

   8. Simplified 59.6%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{x + b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{y} \cdot \color{blue}{\left(x + b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)} \]

      3. flip3-+ N/A

         \[\leadsto \frac{1}{y} \cdot \frac{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}{\color{blue}{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{y} \cdot \frac{1}{\color{blue}{\frac{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}}} \]

      5. un-div-inv N/A

         \[\leadsto \frac{\frac{1}{y}}{\color{blue}{\frac{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{y}\right), \color{blue}{\left(\frac{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}\right)}\right) \]

   10. Applied egg-rr 59.6%

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

   11. Taylor expanded in b around inf

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \color{blue}{\left(\frac{18 \cdot \frac{1}{{b}^{3} \cdot x} - \left(6 \cdot \frac{1}{x} + \left(18 \cdot \frac{1}{{b}^{2} \cdot x} + \frac{18}{b \cdot x}\right)\right)}{{b}^{3}}\right)}\right) \]
   12. Step-by-step derivation

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \mathsf{/.f64}\left(\left(18 \cdot \frac{1}{{b}^{3} \cdot x} - \left(6 \cdot \frac{1}{x} + \left(18 \cdot \frac{1}{{b}^{2} \cdot x} + \frac{18}{b \cdot x}\right)\right)\right), \color{blue}{\left({b}^{3}\right)}\right)\right) \]

   13. Simplified 68.2%

       \[\leadsto \frac{\frac{1}{y}}{\color{blue}{\frac{\frac{18}{b \cdot \left(x \cdot \left(b \cdot b\right)\right)} - \left(\frac{6}{x} + \left(\frac{18}{x \cdot b} + \frac{18}{x \cdot \left(b \cdot b\right)}\right)\right)}{b \cdot \left(b \cdot b\right)}}} \]

   if -8.20000000000000045e-133 < b < -2.6000000000000001e-238

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in b around 0

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

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

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

      2. exp-to-pow N/A

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 81.3%

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

   8. Simplified 81.3%

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

   9. Taylor expanded in t around 0

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

       1. /-lowering-/.f64 63.0%

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

   11. Simplified 63.0%

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

   if -2.6000000000000001e-238 < b < 6.59999999999999976e-255

   1. Initial program 94.4%

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

   3. Taylor expanded in 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 13.5%

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

   5. Simplified 13.5%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 13.5%

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

   8. Simplified 13.5%

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

   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-*r/ N/A

          \[\leadsto \frac{\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(x \cdot \frac{1}{2}\right)}{y} \]

       4. *-commutative N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(\frac{1}{2} \cdot x\right)}{y} \]

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

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

       6. *-commutative N/A

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

       7. associate-*r* N/A

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

       8. *-commutative N/A

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

       9. associate-*l* N/A

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

       10. *-commutative N/A

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

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

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

       12. *-commutative N/A

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

       13. unpow2 N/A

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

       14. associate-*r* N/A

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

       15. *-commutative N/A

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

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

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

       17. *-commutative N/A

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

       18. *-lowering-*.f64 64.0%

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

   11. Simplified 64.0%

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

   if 6.59999999999999976e-255 < b < 1.05e11

   1. Initial program 92.1%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in b around 0

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

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

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

      2. exp-to-pow N/A

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 74.0%

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

   8. Simplified 74.0%

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

   9. Taylor expanded in t around 0

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

       1. *-commutative N/A

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

       2. associate-/r* N/A

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

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

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

       4. /-lowering-/.f64 50.6%

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

   11. Simplified 50.6%

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

   if 1.05e11 < 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 82.0%

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

   5. Simplified 82.0%

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

      1. sub0-neg N/A

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

      2. exp-neg N/A

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

      3. div-inv N/A

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

      4. clear-num N/A

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. exp-lowering-exp.f64 82.0%

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

   7. Applied egg-rr 82.0%

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

   8. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 73.9%

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

   10. Simplified 73.9%

       \[\leadsto \frac{\frac{1}{\frac{\color{blue}{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}}{x}}}{y} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 12: 51.2% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-133}:\\ \;\;\;\;\frac{\frac{-1}{y}}{\frac{\frac{6}{x} + \left(\frac{18}{x \cdot b} + \frac{18}{x \cdot \left(b \cdot b\right)}\right)}{b \cdot \left(b \cdot b\right)}}\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-236}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-260}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 75000000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4e-133)
   (/
    (/ -1.0 y)
    (/
     (+ (/ 6.0 x) (+ (/ 18.0 (* x b)) (/ 18.0 (* x (* b b)))))
     (* b (* b b))))
   (if (<= b -9.5e-236)
     (/ (/ x a) y)
     (if (<= b 1.6e-260)
       (/ (* x (* b (* b 0.5))) y)
       (if (<= b 75000000000000.0)
         (/ (/ x y) a)
         (/
          (/
           1.0
           (/ (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))) x))
          y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4e-133) {
		tmp = (-1.0 / y) / (((6.0 / x) + ((18.0 / (x * b)) + (18.0 / (x * (b * b))))) / (b * (b * b)));
	} else if (b <= -9.5e-236) {
		tmp = (x / a) / y;
	} else if (b <= 1.6e-260) {
		tmp = (x * (b * (b * 0.5))) / y;
	} else if (b <= 75000000000000.0) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))) / x)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4d-133)) then
        tmp = ((-1.0d0) / y) / (((6.0d0 / x) + ((18.0d0 / (x * b)) + (18.0d0 / (x * (b * b))))) / (b * (b * b)))
    else if (b <= (-9.5d-236)) then
        tmp = (x / a) / y
    else if (b <= 1.6d-260) then
        tmp = (x * (b * (b * 0.5d0))) / y
    else if (b <= 75000000000000.0d0) then
        tmp = (x / y) / a
    else
        tmp = (1.0d0 / ((1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0)))))) / x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4e-133) {
		tmp = (-1.0 / y) / (((6.0 / x) + ((18.0 / (x * b)) + (18.0 / (x * (b * b))))) / (b * (b * b)));
	} else if (b <= -9.5e-236) {
		tmp = (x / a) / y;
	} else if (b <= 1.6e-260) {
		tmp = (x * (b * (b * 0.5))) / y;
	} else if (b <= 75000000000000.0) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))) / x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4e-133:
		tmp = (-1.0 / y) / (((6.0 / x) + ((18.0 / (x * b)) + (18.0 / (x * (b * b))))) / (b * (b * b)))
	elif b <= -9.5e-236:
		tmp = (x / a) / y
	elif b <= 1.6e-260:
		tmp = (x * (b * (b * 0.5))) / y
	elif b <= 75000000000000.0:
		tmp = (x / y) / a
	else:
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))) / x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4e-133)
		tmp = Float64(Float64(-1.0 / y) / Float64(Float64(Float64(6.0 / x) + Float64(Float64(18.0 / Float64(x * b)) + Float64(18.0 / Float64(x * Float64(b * b))))) / Float64(b * Float64(b * b))));
	elseif (b <= -9.5e-236)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 1.6e-260)
		tmp = Float64(Float64(x * Float64(b * Float64(b * 0.5))) / y);
	elseif (b <= 75000000000000.0)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))) / x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4e-133)
		tmp = (-1.0 / y) / (((6.0 / x) + ((18.0 / (x * b)) + (18.0 / (x * (b * b))))) / (b * (b * b)));
	elseif (b <= -9.5e-236)
		tmp = (x / a) / y;
	elseif (b <= 1.6e-260)
		tmp = (x * (b * (b * 0.5))) / y;
	elseif (b <= 75000000000000.0)
		tmp = (x / y) / a;
	else
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))) / x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4e-133], N[(N[(-1.0 / y), $MachinePrecision] / N[(N[(N[(6.0 / x), $MachinePrecision] + N[(N[(18.0 / N[(x * b), $MachinePrecision]), $MachinePrecision] + N[(18.0 / N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.5e-236], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.6e-260], N[(N[(x * N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 75000000000000.0], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(1.0 / N[(N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.0000000000000003e-133

   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 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 67.9%

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

   5. Simplified 67.9%

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

   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 59.6%

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

   8. Simplified 59.6%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{x + b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{y} \cdot \color{blue}{\left(x + b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)} \]

      3. flip3-+ N/A

         \[\leadsto \frac{1}{y} \cdot \frac{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}{\color{blue}{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{y} \cdot \frac{1}{\color{blue}{\frac{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}}} \]

      5. un-div-inv N/A

         \[\leadsto \frac{\frac{1}{y}}{\color{blue}{\frac{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{y}\right), \color{blue}{\left(\frac{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}\right)}\right) \]

   10. Applied egg-rr 59.6%

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

   11. Taylor expanded in b around -inf

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \color{blue}{\left(-1 \cdot \frac{6 \cdot \frac{1}{x} + \left(\frac{18}{b \cdot x} + \frac{18}{{b}^{2} \cdot x}\right)}{{b}^{3}}\right)}\right) \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(\mathsf{neg}\left(\frac{6 \cdot \frac{1}{x} + \left(\frac{18}{b \cdot x} + \frac{18}{{b}^{2} \cdot x}\right)}{{b}^{3}}\right)\right)\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(\mathsf{neg}\left(\frac{6 \cdot \frac{1}{x} + \left(\frac{18 \cdot 1}{b \cdot x} + \frac{18}{{b}^{2} \cdot x}\right)}{{b}^{3}}\right)\right)\right) \]

       3. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(\mathsf{neg}\left(\frac{6 \cdot \frac{1}{x} + \left(18 \cdot \frac{1}{b \cdot x} + \frac{18}{{b}^{2} \cdot x}\right)}{{b}^{3}}\right)\right)\right) \]

       4. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(\mathsf{neg}\left(\frac{6 \cdot \frac{1}{x} + \left(18 \cdot \frac{1}{b \cdot x} + \frac{18 \cdot 1}{{b}^{2} \cdot x}\right)}{{b}^{3}}\right)\right)\right) \]

       5. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(\mathsf{neg}\left(\frac{6 \cdot \frac{1}{x} + \left(18 \cdot \frac{1}{b \cdot x} + 18 \cdot \frac{1}{{b}^{2} \cdot x}\right)}{{b}^{3}}\right)\right)\right) \]

       6. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(\mathsf{neg}\left(\frac{6 \cdot \frac{1}{x} + \left(18 \cdot \frac{1}{{b}^{2} \cdot x} + 18 \cdot \frac{1}{b \cdot x}\right)}{{b}^{3}}\right)\right)\right) \]

       7. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(\mathsf{neg}\left(\frac{6 \cdot \frac{1}{x} + \left(18 \cdot \frac{1}{{b}^{2} \cdot x} + \frac{18 \cdot 1}{b \cdot x}\right)}{{b}^{3}}\right)\right)\right) \]

       8. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(\mathsf{neg}\left(\frac{6 \cdot \frac{1}{x} + \left(18 \cdot \frac{1}{{b}^{2} \cdot x} + \frac{18}{b \cdot x}\right)}{{b}^{3}}\right)\right)\right) \]

       9. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(\frac{6 \cdot \frac{1}{x} + \left(18 \cdot \frac{1}{{b}^{2} \cdot x} + \frac{18}{b \cdot x}\right)}{\color{blue}{\mathsf{neg}\left({b}^{3}\right)}}\right)\right) \]

       10. mul-1-neg N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(\frac{6 \cdot \frac{1}{x} + \left(18 \cdot \frac{1}{{b}^{2} \cdot x} + \frac{18}{b \cdot x}\right)}{-1 \cdot \color{blue}{{b}^{3}}}\right)\right) \]

   13. Simplified 67.7%

       \[\leadsto \frac{\frac{1}{y}}{\color{blue}{\frac{\frac{6}{x} + \left(\frac{18}{x \cdot b} + \frac{18}{x \cdot \left(b \cdot b\right)}\right)}{-b \cdot \left(b \cdot b\right)}}} \]

   if -4.0000000000000003e-133 < b < -9.50000000000000065e-236

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in b around 0

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

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

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

      2. exp-to-pow N/A

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 81.3%

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

   8. Simplified 81.3%

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

   9. Taylor expanded in t around 0

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

       1. /-lowering-/.f64 63.0%

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

   11. Simplified 63.0%

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

   if -9.50000000000000065e-236 < b < 1.59999999999999997e-260

   1. Initial program 94.4%

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

   3. Taylor expanded in 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 13.5%

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

   5. Simplified 13.5%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 13.5%

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

   8. Simplified 13.5%

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

   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-*r/ N/A

          \[\leadsto \frac{\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(x \cdot \frac{1}{2}\right)}{y} \]

       4. *-commutative N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(\frac{1}{2} \cdot x\right)}{y} \]

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

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

       6. *-commutative N/A

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

       7. associate-*r* N/A

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

       8. *-commutative N/A

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

       9. associate-*l* N/A

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

       10. *-commutative N/A

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

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

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

       12. *-commutative N/A

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

       13. unpow2 N/A

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

       14. associate-*r* N/A

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

       15. *-commutative N/A

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

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

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

       17. *-commutative N/A

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

       18. *-lowering-*.f64 64.0%

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

   11. Simplified 64.0%

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

   if 1.59999999999999997e-260 < b < 7.5e13

   1. Initial program 92.1%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in b around 0

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

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

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

      2. exp-to-pow N/A

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 74.0%

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

   8. Simplified 74.0%

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

   9. Taylor expanded in t around 0

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

       1. *-commutative N/A

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

       2. associate-/r* N/A

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

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

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

       4. /-lowering-/.f64 50.6%

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

   11. Simplified 50.6%

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

   if 7.5e13 < 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 82.0%

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

   5. Simplified 82.0%

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

      1. sub0-neg N/A

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

      2. exp-neg N/A

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

      3. div-inv N/A

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

      4. clear-num N/A

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. exp-lowering-exp.f64 82.0%

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

   7. Applied egg-rr 82.0%

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

   8. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 73.9%

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

   10. Simplified 73.9%

       \[\leadsto \frac{\frac{1}{\frac{\color{blue}{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}}{x}}}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-133}:\\ \;\;\;\;\frac{\frac{-1}{y}}{\frac{\frac{6}{x} + \left(\frac{18}{x \cdot b} + \frac{18}{x \cdot \left(b \cdot b\right)}\right)}{b \cdot \left(b \cdot b\right)}}\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-236}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-260}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 75000000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}{x}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.5% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -80000000000000:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-237}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{-260}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -80000000000000.0)
   (* x (/ (+ 1.0 (* b (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666)))))) y))
   (if (<= b -4.4e-237)
     (/ (/ x a) y)
     (if (<= b 1.16e-260)
       (/ (* x (* b (* b 0.5))) y)
       (if (<= b 3.7e+14)
         (/ (/ x y) a)
         (/
          (/
           1.0
           (/ (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))) x))
          y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -80000000000000.0) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y);
	} else if (b <= -4.4e-237) {
		tmp = (x / a) / y;
	} else if (b <= 1.16e-260) {
		tmp = (x * (b * (b * 0.5))) / y;
	} else if (b <= 3.7e+14) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))) / x)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-80000000000000.0d0)) then
        tmp = x * ((1.0d0 + (b * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0))))))) / y)
    else if (b <= (-4.4d-237)) then
        tmp = (x / a) / y
    else if (b <= 1.16d-260) then
        tmp = (x * (b * (b * 0.5d0))) / y
    else if (b <= 3.7d+14) then
        tmp = (x / y) / a
    else
        tmp = (1.0d0 / ((1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0)))))) / x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -80000000000000.0) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y);
	} else if (b <= -4.4e-237) {
		tmp = (x / a) / y;
	} else if (b <= 1.16e-260) {
		tmp = (x * (b * (b * 0.5))) / y;
	} else if (b <= 3.7e+14) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))) / x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -80000000000000.0:
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y)
	elif b <= -4.4e-237:
		tmp = (x / a) / y
	elif b <= 1.16e-260:
		tmp = (x * (b * (b * 0.5))) / y
	elif b <= 3.7e+14:
		tmp = (x / y) / a
	else:
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))) / x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -80000000000000.0)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666)))))) / y));
	elseif (b <= -4.4e-237)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 1.16e-260)
		tmp = Float64(Float64(x * Float64(b * Float64(b * 0.5))) / y);
	elseif (b <= 3.7e+14)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))) / x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -80000000000000.0)
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y);
	elseif (b <= -4.4e-237)
		tmp = (x / a) / y;
	elseif (b <= 1.16e-260)
		tmp = (x * (b * (b * 0.5))) / y;
	elseif (b <= 3.7e+14)
		tmp = (x / y) / a;
	else
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))) / x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -80000000000000.0], N[(x * N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.4e-237], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.16e-260], N[(N[(x * N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.7e+14], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(1.0 / N[(N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -8e13

   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 88.8%

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

   5. Simplified 88.8%

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

   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 76.6%

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

   8. Simplified 76.6%

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

   9. Taylor expanded in x around 0

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

       1. associate-/l* N/A

          \[\leadsto x \cdot \color{blue}{\frac{1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)}{y}} \]

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

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

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

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

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

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

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

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

       6. sub-neg N/A

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

       7. metadata-eval N/A

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

       8. +-commutative N/A

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

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

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

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

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

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

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

       12. *-commutative N/A

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

       13. *-lowering-*.f64 83.3%

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

   11. Simplified 83.3%

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

   if -8e13 < b < -4.39999999999999996e-237

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in b around 0

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

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

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

      2. exp-to-pow N/A

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 75.5%

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

   8. Simplified 75.5%

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

   9. Taylor expanded in t around 0

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

       1. /-lowering-/.f64 43.8%

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

   11. Simplified 43.8%

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

   if -4.39999999999999996e-237 < b < 1.15999999999999994e-260

   1. Initial program 94.4%

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

   3. Taylor expanded in 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 13.5%

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

   5. Simplified 13.5%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 13.5%

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

   8. Simplified 13.5%

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

   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-*r/ N/A

          \[\leadsto \frac{\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(x \cdot \frac{1}{2}\right)}{y} \]

       4. *-commutative N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(\frac{1}{2} \cdot x\right)}{y} \]

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

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

       6. *-commutative N/A

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

       7. associate-*r* N/A

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

       8. *-commutative N/A

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

       9. associate-*l* N/A

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

       10. *-commutative N/A

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

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

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

       12. *-commutative N/A

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

       13. unpow2 N/A

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

       14. associate-*r* N/A

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

       15. *-commutative N/A

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

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

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

       17. *-commutative N/A

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

       18. *-lowering-*.f64 64.0%

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

   11. Simplified 64.0%

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

   if 1.15999999999999994e-260 < b < 3.7e14

   1. Initial program 92.1%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in b around 0

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

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

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

      2. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 74.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

   8. Simplified 74.0%

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

       2. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{y}}{\color{blue}{a}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{a}\right) \]

       4. /-lowering-/.f64 50.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), a\right) \]

   11. Simplified 50.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   if 3.7e14 < 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 82.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 82.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      2. exp-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{x}}\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1 \cdot -1}{\frac{e^{b}}{x}}\right), y\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot -1\right), \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(e^{b}\right), x\right)\right), y\right) \]

      9. exp-lowering-exp.f64 82.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), x\right)\right), y\right) \]

   7. Applied egg-rr 82.0%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{e^{b}}{x}}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)}, x\right)\right), y\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right), x\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right), x\right)\right), y\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right), x\right)\right), y\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right), x\right)\right), y\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right), x\right)\right), y\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{1}{6}\right)\right)\right)\right)\right)\right), x\right)\right), y\right) \]

      7. *-lowering-*.f64 73.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right)\right)\right)\right)\right), x\right)\right), y\right) \]

   10. Simplified 73.9%

       \[\leadsto \frac{\frac{1}{\frac{\color{blue}{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}}{x}}}{y} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 14: 51.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -13500000000000:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-236}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-255}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b \cdot \left(1 + b \cdot 0.5\right)}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -13500000000000.0)
   (* x (/ (+ 1.0 (* b (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666)))))) y))
   (if (<= b -2.7e-236)
     (/ (/ x a) y)
     (if (<= b 3.8e-255)
       (/ (* x (* b (* b 0.5))) y)
       (if (<= b 1.25e+26)
         (/ (/ x y) a)
         (/ (/ 1.0 (/ (+ 1.0 (* b (+ 1.0 (* b 0.5)))) x)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -13500000000000.0) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y);
	} else if (b <= -2.7e-236) {
		tmp = (x / a) / y;
	} else if (b <= 3.8e-255) {
		tmp = (x * (b * (b * 0.5))) / y;
	} else if (b <= 1.25e+26) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * 0.5)))) / x)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-13500000000000.0d0)) then
        tmp = x * ((1.0d0 + (b * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0))))))) / y)
    else if (b <= (-2.7d-236)) then
        tmp = (x / a) / y
    else if (b <= 3.8d-255) then
        tmp = (x * (b * (b * 0.5d0))) / y
    else if (b <= 1.25d+26) then
        tmp = (x / y) / a
    else
        tmp = (1.0d0 / ((1.0d0 + (b * (1.0d0 + (b * 0.5d0)))) / x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -13500000000000.0) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y);
	} else if (b <= -2.7e-236) {
		tmp = (x / a) / y;
	} else if (b <= 3.8e-255) {
		tmp = (x * (b * (b * 0.5))) / y;
	} else if (b <= 1.25e+26) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * 0.5)))) / x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -13500000000000.0:
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y)
	elif b <= -2.7e-236:
		tmp = (x / a) / y
	elif b <= 3.8e-255:
		tmp = (x * (b * (b * 0.5))) / y
	elif b <= 1.25e+26:
		tmp = (x / y) / a
	else:
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * 0.5)))) / x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -13500000000000.0)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666)))))) / y));
	elseif (b <= -2.7e-236)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 3.8e-255)
		tmp = Float64(Float64(x * Float64(b * Float64(b * 0.5))) / y);
	elseif (b <= 1.25e+26)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))) / x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -13500000000000.0)
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y);
	elseif (b <= -2.7e-236)
		tmp = (x / a) / y;
	elseif (b <= 3.8e-255)
		tmp = (x * (b * (b * 0.5))) / y;
	elseif (b <= 1.25e+26)
		tmp = (x / y) / a;
	else
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * 0.5)))) / x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -13500000000000.0], N[(x * N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.7e-236], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.8e-255], N[(N[(x * N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.25e+26], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(1.0 / N[(N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.35e13

   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 88.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 88.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   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 76.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 76.6%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}{y}} \]
   10. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto x \cdot \color{blue}{\frac{1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)}{y}} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)}{y}\right)}\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right), \color{blue}{y}\right)\right) \]

       4. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right), y\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right), y\right)\right) \]

       6. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right)\right) \]

       7. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + -1\right)\right)\right), y\right)\right) \]

       8. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(-1 + b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right), y\right)\right) \]

       9. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right), y\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right), y\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right)\right)\right), y\right)\right) \]

       13. *-lowering-*.f64 83.3%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right)\right)\right), y\right)\right) \]

   11. Simplified 83.3%

       \[\leadsto \color{blue}{x \cdot \frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y}} \]

   if -1.35e13 < b < -2.7e-236

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 72.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 72.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      2. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 75.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

   8. Simplified 75.5%

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{a}\right)}, y\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 43.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right) \]

   11. Simplified 43.8%

       \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if -2.7e-236 < b < 3.8e-255

   1. Initial program 94.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in 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 13.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 13.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(-1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \left(\frac{1}{2} \cdot b\right)\right)\right)\right)\right), y\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \left(b \cdot \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 13.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

   8. Simplified 13.5%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}}{y} \]

   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-*r/ N/A

          \[\leadsto \frac{\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(x \cdot \frac{1}{2}\right)}{y} \]

       4. *-commutative N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(\frac{1}{2} \cdot x\right)}{y} \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left({b}^{2} \cdot \left(\frac{1}{2} \cdot x\right)\right), \color{blue}{y}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left({b}^{2} \cdot \left(x \cdot \frac{1}{2}\right)\right), y\right) \]

       7. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}\right), y\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(x \cdot {b}^{2}\right) \cdot \frac{1}{2}\right), y\right) \]

       9. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left({b}^{2} \cdot \frac{1}{2}\right)\right), y\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right), y\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot {b}^{2}\right)\right), y\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({b}^{2} \cdot \frac{1}{2}\right)\right), y\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot b\right) \cdot \frac{1}{2}\right)\right), y\right) \]

       14. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot \frac{1}{2}\right)\right)\right), y\right) \]

       15. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(\frac{1}{2} \cdot b\right)\right)\right), y\right) \]

       16. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot b\right)\right)\right), y\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \frac{1}{2}\right)\right)\right), y\right) \]

       18. *-lowering-*.f64 64.0%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right), y\right) \]

   11. Simplified 64.0%

       \[\leadsto \color{blue}{\frac{x \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)}{y}} \]

   if 3.8e-255 < b < 1.25e26

   1. Initial program 92.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 74.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 74.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      2. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 73.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

   8. Simplified 73.2%

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

       2. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{y}}{\color{blue}{a}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{a}\right) \]

       4. /-lowering-/.f64 50.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), a\right) \]

   11. Simplified 50.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   if 1.25e26 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 81.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      2. exp-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{x}}\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1 \cdot -1}{\frac{e^{b}}{x}}\right), y\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot -1\right), \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(e^{b}\right), x\right)\right), y\right) \]

      9. exp-lowering-exp.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), x\right)\right), y\right) \]

   7. Applied egg-rr 81.3%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{e^{b}}{x}}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\color{blue}{\left(1 + b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)}, x\right)\right), y\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)\right), x\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(1 + \frac{1}{2} \cdot b\right)\right)\right), x\right)\right), y\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(\frac{1}{2} \cdot b\right)\right)\right)\right), x\right)\right), y\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \frac{1}{2}\right)\right)\right)\right), x\right)\right), y\right) \]

      5. *-lowering-*.f64 61.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right), x\right)\right), y\right) \]

   10. Simplified 61.7%

       \[\leadsto \frac{\frac{1}{\frac{\color{blue}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}{x}}}{y} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 15: 43.5% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)}{y}\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.1 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* b (* b 0.5))) y)))
   (if (<= b -6.5e+20)
     t_1
     (if (<= b -8.6e-239)
       (/ (/ x a) y)
       (if (<= b 3.6e-255)
         t_1
         (if (<= b 8.1e+31) (/ (/ x y) a) (/ (/ 1.0 (/ (+ 1.0 b) x)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (b * (b * 0.5))) / y;
	double tmp;
	if (b <= -6.5e+20) {
		tmp = t_1;
	} else if (b <= -8.6e-239) {
		tmp = (x / a) / y;
	} else if (b <= 3.6e-255) {
		tmp = t_1;
	} else if (b <= 8.1e+31) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + b) / x)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (b * (b * 0.5d0))) / y
    if (b <= (-6.5d+20)) then
        tmp = t_1
    else if (b <= (-8.6d-239)) then
        tmp = (x / a) / y
    else if (b <= 3.6d-255) then
        tmp = t_1
    else if (b <= 8.1d+31) then
        tmp = (x / y) / a
    else
        tmp = (1.0d0 / ((1.0d0 + b) / x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (b * (b * 0.5))) / y;
	double tmp;
	if (b <= -6.5e+20) {
		tmp = t_1;
	} else if (b <= -8.6e-239) {
		tmp = (x / a) / y;
	} else if (b <= 3.6e-255) {
		tmp = t_1;
	} else if (b <= 8.1e+31) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + b) / x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (b * (b * 0.5))) / y
	tmp = 0
	if b <= -6.5e+20:
		tmp = t_1
	elif b <= -8.6e-239:
		tmp = (x / a) / y
	elif b <= 3.6e-255:
		tmp = t_1
	elif b <= 8.1e+31:
		tmp = (x / y) / a
	else:
		tmp = (1.0 / ((1.0 + b) / x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(b * Float64(b * 0.5))) / y)
	tmp = 0.0
	if (b <= -6.5e+20)
		tmp = t_1;
	elseif (b <= -8.6e-239)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 3.6e-255)
		tmp = t_1;
	elseif (b <= 8.1e+31)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + b) / x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (b * (b * 0.5))) / y;
	tmp = 0.0;
	if (b <= -6.5e+20)
		tmp = t_1;
	elseif (b <= -8.6e-239)
		tmp = (x / a) / y;
	elseif (b <= 3.6e-255)
		tmp = t_1;
	elseif (b <= 8.1e+31)
		tmp = (x / y) / a;
	else
		tmp = (1.0 / ((1.0 + b) / x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -6.5e+20], t$95$1, If[LessEqual[b, -8.6e-239], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.6e-255], t$95$1, If[LessEqual[b, 8.1e+31], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(1.0 / N[(N[(1.0 + b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.5e20 or -8.6000000000000001e-239 < b < 3.6000000000000002e-255

   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 73.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 73.2%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(-1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \left(\frac{1}{2} \cdot b\right)\right)\right)\right)\right), y\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \left(b \cdot \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 63.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

   8. Simplified 63.3%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}}{y} \]

   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-*r/ N/A

          \[\leadsto \frac{\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(x \cdot \frac{1}{2}\right)}{y} \]

       4. *-commutative N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(\frac{1}{2} \cdot x\right)}{y} \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left({b}^{2} \cdot \left(\frac{1}{2} \cdot x\right)\right), \color{blue}{y}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left({b}^{2} \cdot \left(x \cdot \frac{1}{2}\right)\right), y\right) \]

       7. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}\right), y\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(x \cdot {b}^{2}\right) \cdot \frac{1}{2}\right), y\right) \]

       9. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left({b}^{2} \cdot \frac{1}{2}\right)\right), y\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right), y\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot {b}^{2}\right)\right), y\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({b}^{2} \cdot \frac{1}{2}\right)\right), y\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot b\right) \cdot \frac{1}{2}\right)\right), y\right) \]

       14. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot \frac{1}{2}\right)\right)\right), y\right) \]

       15. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(\frac{1}{2} \cdot b\right)\right)\right), y\right) \]

       16. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot b\right)\right)\right), y\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \frac{1}{2}\right)\right)\right), y\right) \]

       18. *-lowering-*.f64 74.4%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right), y\right) \]

   11. Simplified 74.4%

       \[\leadsto \color{blue}{\frac{x \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)}{y}} \]

   if -6.5e20 < b < -8.6000000000000001e-239

   1. Initial program 98.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 72.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 72.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      2. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 72.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

   8. Simplified 72.9%

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{a}\right)}, y\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 42.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right) \]

   11. Simplified 42.3%

       \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 3.6000000000000002e-255 < b < 8.1e31

   1. Initial program 92.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 74.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 74.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      2. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 73.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

   8. Simplified 73.2%

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

       2. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{y}}{\color{blue}{a}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{a}\right) \]

       4. /-lowering-/.f64 50.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), a\right) \]

   11. Simplified 50.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   if 8.1e31 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 81.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      2. exp-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{x}}\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1 \cdot -1}{\frac{e^{b}}{x}}\right), y\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot -1\right), \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(e^{b}\right), x\right)\right), y\right) \]

      9. exp-lowering-exp.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), x\right)\right), y\right) \]

   7. Applied egg-rr 81.3%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{e^{b}}{x}}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\color{blue}{\left(1 + b\right)}, x\right)\right), y\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(b + 1\right), x\right)\right), y\right) \]

      2. +-lowering-+.f64 30.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, 1\right), x\right)\right), y\right) \]

   10. Simplified 30.0%

       \[\leadsto \frac{\frac{1}{\frac{\color{blue}{b + 1}}{x}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-255}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 8.1 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b}{x}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.9% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.02 \cdot 10^{-260}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b \cdot \left(1 + b \cdot 0.5\right)}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.02e-260)
   (/ (* x (* b (* (* b b) -0.16666666666666666))) y)
   (if (<= b 7.8e+29)
     (/ (/ x y) a)
     (/ (/ 1.0 (/ (+ 1.0 (* b (+ 1.0 (* b 0.5)))) x)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.02e-260) {
		tmp = (x * (b * ((b * b) * -0.16666666666666666))) / y;
	} else if (b <= 7.8e+29) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * 0.5)))) / x)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.02d-260) then
        tmp = (x * (b * ((b * b) * (-0.16666666666666666d0)))) / y
    else if (b <= 7.8d+29) then
        tmp = (x / y) / a
    else
        tmp = (1.0d0 / ((1.0d0 + (b * (1.0d0 + (b * 0.5d0)))) / x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.02e-260) {
		tmp = (x * (b * ((b * b) * -0.16666666666666666))) / y;
	} else if (b <= 7.8e+29) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * 0.5)))) / x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.02e-260:
		tmp = (x * (b * ((b * b) * -0.16666666666666666))) / y
	elif b <= 7.8e+29:
		tmp = (x / y) / a
	else:
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * 0.5)))) / x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.02e-260)
		tmp = Float64(Float64(x * Float64(b * Float64(Float64(b * b) * -0.16666666666666666))) / y);
	elseif (b <= 7.8e+29)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))) / x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.02e-260)
		tmp = (x * (b * ((b * b) * -0.16666666666666666))) / y;
	elseif (b <= 7.8e+29)
		tmp = (x / y) / a;
	else
		tmp = (1.0 / ((1.0 + (b * (1.0 + (b * 0.5)))) / x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.02e-260], N[(N[(x * N[(b * N[(N[(b * b), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 7.8e+29], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(1.0 / N[(N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 1.01999999999999991e-260

   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 54.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 54.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)}, y\right) \]
   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 48.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 48.4%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right) + x\right), y\right) \]

      2. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot x}{b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right) - x}\right), y\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot x\right) \cdot \frac{1}{b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right) - x}\right), y\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot x\right), \left(\frac{1}{b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right) - x}\right)\right), y\right) \]

   10. Applied egg-rr 12.2%

       \[\leadsto \frac{\color{blue}{\left(\left(b \cdot b\right) \cdot \left(\left(x \cdot \left(\left(0.5 + b \cdot -0.16666666666666666\right) \cdot b\right) - x\right) \cdot \left(x \cdot \left(\left(0.5 + b \cdot -0.16666666666666666\right) \cdot b\right) - x\right)\right) - x \cdot x\right) \cdot \frac{1}{b \cdot \left(x \cdot \left(\left(0.5 + b \cdot -0.16666666666666666\right) \cdot b\right) - x\right) - x}}}{y} \]

   11. Taylor expanded in b around inf

       \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)\right)}, y\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{6} \cdot \left(x \cdot {b}^{3}\right)\right), y\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot x\right) \cdot {b}^{3}\right), y\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(x \cdot \frac{-1}{6}\right) \cdot {b}^{3}\right), y\right) \]

       4. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       6. unpow3 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot \left(\left(b \cdot b\right) \cdot b\right)\right)\right), y\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot \left({b}^{2} \cdot b\right)\right)\right), y\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\frac{-1}{6} \cdot {b}^{2}\right) \cdot b\right)\right), y\right) \]

       9. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\frac{-1}{6} \cdot \left(b \cdot b\right)\right) \cdot b\right)\right), y\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\frac{-1}{6} \cdot b\right) \cdot b\right) \cdot b\right)\right), y\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(b \cdot \frac{-1}{6}\right) \cdot b\right) \cdot b\right)\right), y\right) \]

       12. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot \left(\frac{-1}{6} \cdot b\right)\right) \cdot b\right)\right), y\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot b\right)\right), b\right)\right), y\right) \]

       14. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(b \cdot \left(b \cdot \frac{-1}{6}\right)\right), b\right)\right), y\right) \]

       15. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(\left(b \cdot b\right) \cdot \frac{-1}{6}\right), b\right)\right), y\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({b}^{2} \cdot \frac{-1}{6}\right), b\right)\right), y\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({b}^{2}\right), \frac{-1}{6}\right), b\right)\right), y\right) \]

       18. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(b \cdot b\right), \frac{-1}{6}\right), b\right)\right), y\right) \]

       19. *-lowering-*.f64 59.7%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \frac{-1}{6}\right), b\right)\right), y\right) \]

   13. Simplified 59.7%

       \[\leadsto \frac{\color{blue}{x \cdot \left(\left(\left(b \cdot b\right) \cdot -0.16666666666666666\right) \cdot b\right)}}{y} \]

   if 1.01999999999999991e-260 < b < 7.79999999999999937e29

   1. Initial program 92.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 74.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 74.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      2. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 73.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

   8. Simplified 73.2%

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

       2. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{y}}{\color{blue}{a}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{a}\right) \]

       4. /-lowering-/.f64 50.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), a\right) \]

   11. Simplified 50.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   if 7.79999999999999937e29 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 81.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      2. exp-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{x}}\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1 \cdot -1}{\frac{e^{b}}{x}}\right), y\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot -1\right), \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(e^{b}\right), x\right)\right), y\right) \]

      9. exp-lowering-exp.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), x\right)\right), y\right) \]

   7. Applied egg-rr 81.3%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{e^{b}}{x}}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\color{blue}{\left(1 + b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)}, x\right)\right), y\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)\right), x\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(1 + \frac{1}{2} \cdot b\right)\right)\right), x\right)\right), y\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(\frac{1}{2} \cdot b\right)\right)\right)\right), x\right)\right), y\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \frac{1}{2}\right)\right)\right)\right), x\right)\right), y\right) \]

      5. *-lowering-*.f64 61.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right), x\right)\right), y\right) \]

   10. Simplified 61.7%

       \[\leadsto \frac{\frac{1}{\frac{\color{blue}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}{x}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.02 \cdot 10^{-260}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b \cdot \left(1 + b \cdot 0.5\right)}{x}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 40.2% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)}{y}\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-231}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* b (* b 0.5))) y)))
   (if (<= b -1.5e+24)
     t_1
     (if (<= b -3.6e-231)
       (/ (/ x a) y)
       (if (<= b 6.6e-256) t_1 (/ (/ x y) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (b * (b * 0.5))) / y;
	double tmp;
	if (b <= -1.5e+24) {
		tmp = t_1;
	} else if (b <= -3.6e-231) {
		tmp = (x / a) / y;
	} else if (b <= 6.6e-256) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x * (b * (b * 0.5d0))) / y
    if (b <= (-1.5d+24)) then
        tmp = t_1
    else if (b <= (-3.6d-231)) then
        tmp = (x / a) / y
    else if (b <= 6.6d-256) then
        tmp = t_1
    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 t_1 = (x * (b * (b * 0.5))) / y;
	double tmp;
	if (b <= -1.5e+24) {
		tmp = t_1;
	} else if (b <= -3.6e-231) {
		tmp = (x / a) / y;
	} else if (b <= 6.6e-256) {
		tmp = t_1;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (b * (b * 0.5))) / y
	tmp = 0
	if b <= -1.5e+24:
		tmp = t_1
	elif b <= -3.6e-231:
		tmp = (x / a) / y
	elif b <= 6.6e-256:
		tmp = t_1
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(b * Float64(b * 0.5))) / y)
	tmp = 0.0
	if (b <= -1.5e+24)
		tmp = t_1;
	elseif (b <= -3.6e-231)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 6.6e-256)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (b * (b * 0.5))) / y;
	tmp = 0.0;
	if (b <= -1.5e+24)
		tmp = t_1;
	elseif (b <= -3.6e-231)
		tmp = (x / a) / y;
	elseif (b <= 6.6e-256)
		tmp = t_1;
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.5e+24], t$95$1, If[LessEqual[b, -3.6e-231], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6.6e-256], t$95$1, N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.49999999999999997e24 or -3.59999999999999973e-231 < b < 6.6e-256

   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 73.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 73.2%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(-1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \left(\frac{1}{2} \cdot b\right)\right)\right)\right)\right), y\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \left(b \cdot \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 63.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

   8. Simplified 63.3%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}}{y} \]

   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-*r/ N/A

          \[\leadsto \frac{\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(x \cdot \frac{1}{2}\right)}{y} \]

       4. *-commutative N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(\frac{1}{2} \cdot x\right)}{y} \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left({b}^{2} \cdot \left(\frac{1}{2} \cdot x\right)\right), \color{blue}{y}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left({b}^{2} \cdot \left(x \cdot \frac{1}{2}\right)\right), y\right) \]

       7. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}\right), y\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(x \cdot {b}^{2}\right) \cdot \frac{1}{2}\right), y\right) \]

       9. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left({b}^{2} \cdot \frac{1}{2}\right)\right), y\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right), y\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot {b}^{2}\right)\right), y\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({b}^{2} \cdot \frac{1}{2}\right)\right), y\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot b\right) \cdot \frac{1}{2}\right)\right), y\right) \]

       14. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot \frac{1}{2}\right)\right)\right), y\right) \]

       15. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(\frac{1}{2} \cdot b\right)\right)\right), y\right) \]

       16. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot b\right)\right)\right), y\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \frac{1}{2}\right)\right)\right), y\right) \]

       18. *-lowering-*.f64 74.4%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right), y\right) \]

   11. Simplified 74.4%

       \[\leadsto \color{blue}{\frac{x \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)}{y}} \]

   if -1.49999999999999997e24 < b < -3.59999999999999973e-231

   1. Initial program 98.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 72.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 72.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      2. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 72.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

   8. Simplified 72.9%

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{a}\right)}, y\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 42.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right) \]

   11. Simplified 42.3%

       \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 6.6e-256 < b

   1. Initial program 96.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 79.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 79.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      2. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 56.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

   8. Simplified 56.0%

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

       2. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{y}}{\color{blue}{a}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{a}\right) \]

       4. /-lowering-/.f64 30.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), a\right) \]

   11. Simplified 30.5%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 43.2% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.2 \cdot 10^{-259}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.2e-259)
   (/ (* x (* b (* (* b b) -0.16666666666666666))) y)
   (if (<= b 5.5e+38) (/ (/ x y) a) (/ (/ 1.0 (/ (+ 1.0 b) x)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.2e-259) {
		tmp = (x * (b * ((b * b) * -0.16666666666666666))) / y;
	} else if (b <= 5.5e+38) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + b) / x)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.2d-259) then
        tmp = (x * (b * ((b * b) * (-0.16666666666666666d0)))) / y
    else if (b <= 5.5d+38) then
        tmp = (x / y) / a
    else
        tmp = (1.0d0 / ((1.0d0 + b) / x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.2e-259) {
		tmp = (x * (b * ((b * b) * -0.16666666666666666))) / y;
	} else if (b <= 5.5e+38) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + b) / x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.2e-259:
		tmp = (x * (b * ((b * b) * -0.16666666666666666))) / y
	elif b <= 5.5e+38:
		tmp = (x / y) / a
	else:
		tmp = (1.0 / ((1.0 + b) / x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.2e-259)
		tmp = Float64(Float64(x * Float64(b * Float64(Float64(b * b) * -0.16666666666666666))) / y);
	elseif (b <= 5.5e+38)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + b) / x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.2e-259)
		tmp = (x * (b * ((b * b) * -0.16666666666666666))) / y;
	elseif (b <= 5.5e+38)
		tmp = (x / y) / a;
	else
		tmp = (1.0 / ((1.0 + b) / x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.2e-259], N[(N[(x * N[(b * N[(N[(b * b), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5.5e+38], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(1.0 / N[(N[(1.0 + b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 2.2000000000000001e-259

   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 54.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 54.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)}, y\right) \]
   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 48.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 48.4%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right) + x\right), y\right) \]

      2. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot x}{b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right) - x}\right), y\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot x\right) \cdot \frac{1}{b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right) - x}\right), y\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot x\right), \left(\frac{1}{b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right) - x}\right)\right), y\right) \]

   10. Applied egg-rr 12.2%

       \[\leadsto \frac{\color{blue}{\left(\left(b \cdot b\right) \cdot \left(\left(x \cdot \left(\left(0.5 + b \cdot -0.16666666666666666\right) \cdot b\right) - x\right) \cdot \left(x \cdot \left(\left(0.5 + b \cdot -0.16666666666666666\right) \cdot b\right) - x\right)\right) - x \cdot x\right) \cdot \frac{1}{b \cdot \left(x \cdot \left(\left(0.5 + b \cdot -0.16666666666666666\right) \cdot b\right) - x\right) - x}}}{y} \]

   11. Taylor expanded in b around inf

       \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)\right)}, y\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{6} \cdot \left(x \cdot {b}^{3}\right)\right), y\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot x\right) \cdot {b}^{3}\right), y\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(x \cdot \frac{-1}{6}\right) \cdot {b}^{3}\right), y\right) \]

       4. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       6. unpow3 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot \left(\left(b \cdot b\right) \cdot b\right)\right)\right), y\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot \left({b}^{2} \cdot b\right)\right)\right), y\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\frac{-1}{6} \cdot {b}^{2}\right) \cdot b\right)\right), y\right) \]

       9. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\frac{-1}{6} \cdot \left(b \cdot b\right)\right) \cdot b\right)\right), y\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\frac{-1}{6} \cdot b\right) \cdot b\right) \cdot b\right)\right), y\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(b \cdot \frac{-1}{6}\right) \cdot b\right) \cdot b\right)\right), y\right) \]

       12. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot \left(\frac{-1}{6} \cdot b\right)\right) \cdot b\right)\right), y\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot b\right)\right), b\right)\right), y\right) \]

       14. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(b \cdot \left(b \cdot \frac{-1}{6}\right)\right), b\right)\right), y\right) \]

       15. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(\left(b \cdot b\right) \cdot \frac{-1}{6}\right), b\right)\right), y\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({b}^{2} \cdot \frac{-1}{6}\right), b\right)\right), y\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({b}^{2}\right), \frac{-1}{6}\right), b\right)\right), y\right) \]

       18. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(b \cdot b\right), \frac{-1}{6}\right), b\right)\right), y\right) \]

       19. *-lowering-*.f64 59.7%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \frac{-1}{6}\right), b\right)\right), y\right) \]

   13. Simplified 59.7%

       \[\leadsto \frac{\color{blue}{x \cdot \left(\left(\left(b \cdot b\right) \cdot -0.16666666666666666\right) \cdot b\right)}}{y} \]

   if 2.2000000000000001e-259 < b < 5.5000000000000003e38

   1. Initial program 92.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 74.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 74.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      2. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 73.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

   8. Simplified 73.2%

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

       2. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{y}}{\color{blue}{a}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{a}\right) \]

       4. /-lowering-/.f64 50.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), a\right) \]

   11. Simplified 50.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   if 5.5000000000000003e38 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 81.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      2. exp-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{x}}\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1 \cdot -1}{\frac{e^{b}}{x}}\right), y\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot -1\right), \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(e^{b}\right), x\right)\right), y\right) \]

      9. exp-lowering-exp.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), x\right)\right), y\right) \]

   7. Applied egg-rr 81.3%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{e^{b}}{x}}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\color{blue}{\left(1 + b\right)}, x\right)\right), y\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(b + 1\right), x\right)\right), y\right) \]

      2. +-lowering-+.f64 30.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, 1\right), x\right)\right), y\right) \]

   10. Simplified 30.0%

       \[\leadsto \frac{\frac{1}{\frac{\color{blue}{b + 1}}{x}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.2 \cdot 10^{-259}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b}{x}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 42.0% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.7 \cdot 10^{-260}:\\ \;\;\;\;\frac{b \cdot \left(b \cdot \left(x \cdot \left(b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.7e-260)
   (/ (* b (* b (* x (* b -0.16666666666666666)))) y)
   (if (<= b 2.1e+33) (/ (/ x y) a) (/ (/ 1.0 (/ (+ 1.0 b) x)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.7e-260) {
		tmp = (b * (b * (x * (b * -0.16666666666666666)))) / y;
	} else if (b <= 2.1e+33) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + b) / x)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.7d-260) then
        tmp = (b * (b * (x * (b * (-0.16666666666666666d0))))) / y
    else if (b <= 2.1d+33) then
        tmp = (x / y) / a
    else
        tmp = (1.0d0 / ((1.0d0 + b) / x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.7e-260) {
		tmp = (b * (b * (x * (b * -0.16666666666666666)))) / y;
	} else if (b <= 2.1e+33) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + b) / x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.7e-260:
		tmp = (b * (b * (x * (b * -0.16666666666666666)))) / y
	elif b <= 2.1e+33:
		tmp = (x / y) / a
	else:
		tmp = (1.0 / ((1.0 + b) / x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.7e-260)
		tmp = Float64(Float64(b * Float64(b * Float64(x * Float64(b * -0.16666666666666666)))) / y);
	elseif (b <= 2.1e+33)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + b) / x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.7e-260)
		tmp = (b * (b * (x * (b * -0.16666666666666666)))) / y;
	elseif (b <= 2.1e+33)
		tmp = (x / y) / a;
	else
		tmp = (1.0 / ((1.0 + b) / x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.7e-260], N[(N[(b * N[(b * N[(x * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.1e+33], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(1.0 / N[(N[(1.0 + b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 1.6999999999999999e-260

   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 54.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 54.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)}, y\right) \]
   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 48.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 48.4%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   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

          \[\leadsto \frac{\frac{-1}{6} \cdot \left(x \cdot {b}^{3}\right)}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{\left(\frac{-1}{6} \cdot x\right) \cdot {b}^{3}}{y} \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot x\right) \cdot {b}^{3}\right), \color{blue}{y}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left({b}^{3} \cdot \left(\frac{-1}{6} \cdot x\right)\right), y\right) \]

       6. cube-mult N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\frac{-1}{6} \cdot x\right)\right), y\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(b \cdot {b}^{2}\right) \cdot \left(\frac{-1}{6} \cdot x\right)\right), y\right) \]

       8. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(b \cdot \left({b}^{2} \cdot \left(\frac{-1}{6} \cdot x\right)\right)\right), y\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(b \cdot \left(\left(\frac{-1}{6} \cdot x\right) \cdot {b}^{2}\right)\right), y\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(\left(\frac{-1}{6} \cdot x\right) \cdot {b}^{2}\right)\right), y\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left({b}^{2} \cdot \left(\frac{-1}{6} \cdot x\right)\right)\right), y\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(\left(b \cdot b\right) \cdot \left(\frac{-1}{6} \cdot x\right)\right)\right), y\right) \]

       13. associate-*l* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(b \cdot \left(b \cdot \left(\frac{-1}{6} \cdot x\right)\right)\right)\right), y\right) \]

       14. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(b \cdot \left(b \cdot \left(x \cdot \frac{-1}{6}\right)\right)\right)\right), y\right) \]

       15. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(b \cdot \left(\left(b \cdot x\right) \cdot \frac{-1}{6}\right)\right)\right), y\right) \]

       16. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

       18. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(\left(\frac{-1}{6} \cdot b\right) \cdot x\right)\right)\right), y\right) \]

       19. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       20. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       21. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), y\right) \]

       22. *-lowering-*.f64 58.5%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), y\right) \]

   11. Simplified 58.5%

       \[\leadsto \color{blue}{\frac{b \cdot \left(b \cdot \left(x \cdot \left(b \cdot -0.16666666666666666\right)\right)\right)}{y}} \]

   if 1.6999999999999999e-260 < b < 2.1000000000000001e33

   1. Initial program 92.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 74.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 74.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      2. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 73.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

   8. Simplified 73.2%

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

       2. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{y}}{\color{blue}{a}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{a}\right) \]

       4. /-lowering-/.f64 50.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), a\right) \]

   11. Simplified 50.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   if 2.1000000000000001e33 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 81.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      2. exp-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{x}}\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1 \cdot -1}{\frac{e^{b}}{x}}\right), y\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot -1\right), \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(e^{b}\right), x\right)\right), y\right) \]

      9. exp-lowering-exp.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), x\right)\right), y\right) \]

   7. Applied egg-rr 81.3%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{e^{b}}{x}}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\color{blue}{\left(1 + b\right)}, x\right)\right), y\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(b + 1\right), x\right)\right), y\right) \]

      2. +-lowering-+.f64 30.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, 1\right), x\right)\right), y\right) \]

   10. Simplified 30.0%

       \[\leadsto \frac{\frac{1}{\frac{\color{blue}{b + 1}}{x}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.7 \cdot 10^{-260}:\\ \;\;\;\;\frac{b \cdot \left(b \cdot \left(x \cdot \left(b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b}{x}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 41.9% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.7 \cdot 10^{-257}:\\ \;\;\;\;\left(b \cdot b\right) \cdot \frac{b \cdot \left(x \cdot -0.16666666666666666\right)}{y}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.7e-257)
   (* (* b b) (/ (* b (* x -0.16666666666666666)) y))
   (if (<= b 5.5e+41) (/ (/ x y) a) (/ (/ 1.0 (/ (+ 1.0 b) x)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.7e-257) {
		tmp = (b * b) * ((b * (x * -0.16666666666666666)) / y);
	} else if (b <= 5.5e+41) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + b) / x)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.7d-257) then
        tmp = (b * b) * ((b * (x * (-0.16666666666666666d0))) / y)
    else if (b <= 5.5d+41) then
        tmp = (x / y) / a
    else
        tmp = (1.0d0 / ((1.0d0 + b) / x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.7e-257) {
		tmp = (b * b) * ((b * (x * -0.16666666666666666)) / y);
	} else if (b <= 5.5e+41) {
		tmp = (x / y) / a;
	} else {
		tmp = (1.0 / ((1.0 + b) / x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.7e-257:
		tmp = (b * b) * ((b * (x * -0.16666666666666666)) / y)
	elif b <= 5.5e+41:
		tmp = (x / y) / a
	else:
		tmp = (1.0 / ((1.0 + b) / x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.7e-257)
		tmp = Float64(Float64(b * b) * Float64(Float64(b * Float64(x * -0.16666666666666666)) / y));
	elseif (b <= 5.5e+41)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + b) / x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.7e-257)
		tmp = (b * b) * ((b * (x * -0.16666666666666666)) / y);
	elseif (b <= 5.5e+41)
		tmp = (x / y) / a;
	else
		tmp = (1.0 / ((1.0 + b) / x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.7e-257], N[(N[(b * b), $MachinePrecision] * N[(N[(b * N[(x * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+41], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(1.0 / N[(N[(1.0 + b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 3.69999999999999984e-257

   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 54.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 54.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)}, y\right) \]
   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 48.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 48.4%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]
   9. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{x + b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{y} \cdot \color{blue}{\left(x + b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)} \]

      3. flip3-+ N/A

         \[\leadsto \frac{1}{y} \cdot \frac{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}{\color{blue}{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}} \]

      4. clear-num N/A

         \[\leadsto \frac{1}{y} \cdot \frac{1}{\color{blue}{\frac{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}}} \]

      5. un-div-inv N/A

         \[\leadsto \frac{\frac{1}{y}}{\color{blue}{\frac{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}}} \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{y}\right), \color{blue}{\left(\frac{x \cdot x + \left(\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right) - x \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)\right)}{{x}^{3} + {\left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right) - x\right)\right)}^{3}}\right)}\right) \]

   10. Applied egg-rr 48.4%

       \[\leadsto \color{blue}{\frac{\frac{1}{y}}{\frac{1}{x + b \cdot \left(x \cdot \left(\left(0.5 + b \cdot -0.16666666666666666\right) \cdot b\right) - x\right)}}} \]

   11. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{{b}^{3} \cdot x}{y} \cdot \color{blue}{\frac{-1}{6}} \]

       2. associate-/l* N/A

          \[\leadsto \left({b}^{3} \cdot \frac{x}{y}\right) \cdot \frac{-1}{6} \]

       3. associate-*r* N/A

          \[\leadsto {b}^{3} \cdot \color{blue}{\left(\frac{x}{y} \cdot \frac{-1}{6}\right)} \]

       4. *-commutative N/A

          \[\leadsto {b}^{3} \cdot \left(\frac{-1}{6} \cdot \color{blue}{\frac{x}{y}}\right) \]

       5. unpow3 N/A

          \[\leadsto \left(\left(b \cdot b\right) \cdot b\right) \cdot \left(\color{blue}{\frac{-1}{6}} \cdot \frac{x}{y}\right) \]

       6. unpow2 N/A

          \[\leadsto \left({b}^{2} \cdot b\right) \cdot \left(\frac{-1}{6} \cdot \frac{x}{y}\right) \]

       7. associate-*l* N/A

          \[\leadsto {b}^{2} \cdot \color{blue}{\left(b \cdot \left(\frac{-1}{6} \cdot \frac{x}{y}\right)\right)} \]

       8. *-commutative N/A

          \[\leadsto {b}^{2} \cdot \left(b \cdot \left(\frac{x}{y} \cdot \color{blue}{\frac{-1}{6}}\right)\right) \]

       9. associate-*l* N/A

          \[\leadsto {b}^{2} \cdot \left(\left(b \cdot \frac{x}{y}\right) \cdot \color{blue}{\frac{-1}{6}}\right) \]

       10. associate-/l* N/A

           \[\leadsto {b}^{2} \cdot \left(\frac{b \cdot x}{y} \cdot \frac{-1}{6}\right) \]

       11. *-commutative N/A

           \[\leadsto {b}^{2} \cdot \left(\frac{-1}{6} \cdot \color{blue}{\frac{b \cdot x}{y}}\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\left({b}^{2}\right), \color{blue}{\left(\frac{-1}{6} \cdot \frac{b \cdot x}{y}\right)}\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\left(b \cdot b\right), \left(\color{blue}{\frac{-1}{6}} \cdot \frac{b \cdot x}{y}\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(\color{blue}{\frac{-1}{6}} \cdot \frac{b \cdot x}{y}\right)\right) \]

       15. associate-*r/ N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(\frac{\frac{-1}{6} \cdot \left(b \cdot x\right)}{\color{blue}{y}}\right)\right) \]

       16. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \mathsf{/.f64}\left(\left(\frac{-1}{6} \cdot \left(b \cdot x\right)\right), \color{blue}{y}\right)\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \mathsf{/.f64}\left(\left(\left(b \cdot x\right) \cdot \frac{-1}{6}\right), y\right)\right) \]

       18. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \mathsf{/.f64}\left(\left(b \cdot \left(x \cdot \frac{-1}{6}\right)\right), y\right)\right) \]

       19. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \mathsf{/.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot x\right)\right), y\right)\right) \]

       20. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot x\right)\right), y\right)\right) \]

       21. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \frac{-1}{6}\right)\right), y\right)\right) \]

       22. *-lowering-*.f64 58.4%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \frac{-1}{6}\right)\right), y\right)\right) \]

   13. Simplified 58.4%

       \[\leadsto \color{blue}{\left(b \cdot b\right) \cdot \frac{b \cdot \left(x \cdot -0.16666666666666666\right)}{y}} \]

   if 3.69999999999999984e-257 < b < 5.5000000000000003e41

   1. Initial program 92.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 74.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 74.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      2. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 73.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

   8. Simplified 73.2%

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

       2. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{y}}{\color{blue}{a}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{a}\right) \]

       4. /-lowering-/.f64 50.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), a\right) \]

   11. Simplified 50.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   if 5.5000000000000003e41 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 81.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      2. exp-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{x}}\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1 \cdot -1}{\frac{e^{b}}{x}}\right), y\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot -1\right), \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{e^{b}}{x}\right)\right), y\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(e^{b}\right), x\right)\right), y\right) \]

      9. exp-lowering-exp.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), x\right)\right), y\right) \]

   7. Applied egg-rr 81.3%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{e^{b}}{x}}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\color{blue}{\left(1 + b\right)}, x\right)\right), y\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(b + 1\right), x\right)\right), y\right) \]

      2. +-lowering-+.f64 30.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, 1\right), x\right)\right), y\right) \]

   10. Simplified 30.0%

       \[\leadsto \frac{\frac{1}{\frac{\color{blue}{b + 1}}{x}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.7 \cdot 10^{-257}:\\ \;\;\;\;\left(b \cdot b\right) \cdot \frac{b \cdot \left(x \cdot -0.16666666666666666\right)}{y}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1 + b}{x}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 34.1% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+161}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.1e+161) (/ (* 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 <= -1.1e+161) {
		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 <= (-1.1d+161)) 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 <= -1.1e+161) {
		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 <= -1.1e+161:
		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 <= -1.1e+161)
		tmp = Float64(Float64(x * Float64(1.0 - b)) / y);
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.1e+161)
		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, -1.1e+161], N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1e161

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 93.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 93.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   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. neg-mul-1 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(b\right)\right) \cdot x\right), y\right) \]

      3. distribute-rgt1-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(b\right)\right) + 1\right) \cdot x\right), y\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 + \left(\mathsf{neg}\left(b\right)\right)\right) \cdot x\right), y\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 + \left(\mathsf{neg}\left(b\right)\right)\right), x\right), y\right) \]

      6. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 - b\right), x\right), y\right) \]

      7. --lowering--.f64 51.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, b\right), x\right), y\right) \]

   8. Simplified 51.9%

      \[\leadsto \frac{\color{blue}{\left(1 - b\right) \cdot x}}{y} \]

   if -1.1e161 < b

   1. Initial program 97.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 75.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 75.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      2. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 57.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

   8. Simplified 57.8%

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

       2. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{y}}{\color{blue}{a}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{a}\right) \]

       4. /-lowering-/.f64 33.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), a\right) \]

   11. Simplified 33.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+161}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.3% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{y}}{a} \end{array} \]

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(Float64(x / 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[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]

Derivation

1. Initial program 97.6%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
4. Step-by-step derivation

   1. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

   3. log-lowering-log.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

   4. sub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

   6. +-lowering-+.f64 78.7%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

5. Simplified 78.7%

   \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

6. Taylor expanded in b around 0

   \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

   2. exp-to-pow N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

   3. pow-lowering-pow.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

   4. sub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

   6. +-lowering-+.f64 52.5%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

8. Simplified 52.5%

   \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

9. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
10. Step-by-step derivation

    1. *-commutative N/A

       \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

    2. associate-/r* N/A

       \[\leadsto \frac{\frac{x}{y}}{\color{blue}{a}} \]

    3. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{a}\right) \]

    4. /-lowering-/.f64 30.2%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), a\right) \]

11. Simplified 30.2%

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]
12. Add Preprocessing

Alternative 23: 31.3% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (/ x a) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x / a) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x / a) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x / a) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x / a) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 97.6%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
4. Step-by-step derivation

   1. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

   3. log-lowering-log.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

   4. sub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

   6. +-lowering-+.f64 78.7%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

5. Simplified 78.7%

   \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right) - b}}}{y} \]

6. Taylor expanded in b around 0

   \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

   2. exp-to-pow N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), y\right) \]

   3. pow-lowering-pow.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), y\right) \]

   4. sub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), y\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), y\right) \]

   6. +-lowering-+.f64 52.5%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), y\right) \]

8. Simplified 52.5%

   \[\leadsto \frac{\color{blue}{x \cdot {a}^{\left(t + -1\right)}}}{y} \]

9. Taylor expanded in t around 0

   \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{a}\right)}, y\right) \]
10. Step-by-step derivation

    1. /-lowering-/.f64 27.5%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right) \]

11. Simplified 27.5%

    \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]
12. Add Preprocessing

Alternative 24: 17.1% 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 97.6%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in 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 53.6%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

5. Simplified 53.6%

   \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

6. Taylor expanded in b around 0

   \[\leadsto \color{blue}{\frac{x}{y}} \]
7. Step-by-step derivation

   1. /-lowering-/.f64 17.5%

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

8. Simplified 17.5%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Step-by-step derivation

   1. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{y}{x}}} \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{y}{x}\right)}\right) \]

   3. /-lowering-/.f64 17.9%

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

10. Applied egg-rr 17.9%

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]
11. Add Preprocessing

Alternative 25: 16.8% 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 97.6%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in 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 53.6%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

5. Simplified 53.6%

   \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

6. Taylor expanded in b around 0

   \[\leadsto \color{blue}{\frac{x}{y}} \]
7. Step-by-step derivation

   1. /-lowering-/.f64 17.5%

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

8. Simplified 17.5%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Add Preprocessing

Developer Target 1: 72.3% 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 2024158 
(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))