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

Percentage Accurate: 98.3% → 98.3%

Time: 18.3s

Alternatives: 25

Speedup: 1.0×

• 47.7% 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: 98.3% 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: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.9%

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

Alternative 2: 90.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(y \cdot \log z + \log a \cdot t\right) - b}}{y}\\ \mathbf{if}\;y \leq -0.07:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-304}:\\ \;\;\;\;\frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (+ (* y (log z)) (* (log a) t)) b))) y)))
   (if (<= y -0.07)
     t_1
     (if (<= y 1.6e-304) (/ (* (/ (pow a (+ t -1.0)) (exp b)) x) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp((((y * log(z)) + (log(a) * t)) - b))) / y;
	double tmp;
	if (y <= -0.07) {
		tmp = t_1;
	} else if (y <= 1.6e-304) {
		tmp = ((pow(a, (t + -1.0)) / exp(b)) * 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((((y * log(z)) + (log(a) * t)) - b))) / y
    if (y <= (-0.07d0)) then
        tmp = t_1
    else if (y <= 1.6d-304) then
        tmp = (((a ** (t + (-1.0d0))) / exp(b)) * 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((((y * Math.log(z)) + (Math.log(a) * t)) - b))) / y;
	double tmp;
	if (y <= -0.07) {
		tmp = t_1;
	} else if (y <= 1.6e-304) {
		tmp = ((Math.pow(a, (t + -1.0)) / Math.exp(b)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp((((y * math.log(z)) + (math.log(a) * t)) - b))) / y
	tmp = 0
	if y <= -0.07:
		tmp = t_1
	elif y <= 1.6e-304:
		tmp = ((math.pow(a, (t + -1.0)) / math.exp(b)) * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(log(a) * t)) - b))) / y)
	tmp = 0.0
	if (y <= -0.07)
		tmp = t_1;
	elseif (y <= 1.6e-304)
		tmp = Float64(Float64(Float64((a ^ Float64(t + -1.0)) / exp(b)) * 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((((y * log(z)) + (log(a) * t)) - b))) / y;
	tmp = 0.0;
	if (y <= -0.07)
		tmp = t_1;
	elseif (y <= 1.6e-304)
		tmp = (((a ^ (t + -1.0)) / exp(b)) * 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[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -0.07], t$95$1, If[LessEqual[y, 1.6e-304], N[(N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.070000000000000007 or 1.59999999999999999e-304 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -0.070000000000000007 < y < 1.59999999999999999e-304

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 81.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+25}:\\ \;\;\;\;\frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -5.8e+69)
     t_1
     (if (<= y 5.2e+25) (/ (* (/ (pow a (+ t -1.0)) (exp b)) x) 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 <= -5.8e+69) {
		tmp = t_1;
	} else if (y <= 5.2e+25) {
		tmp = ((pow(a, (t + -1.0)) / exp(b)) * 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 * (z ** y)) / a) / y
    if (y <= (-5.8d+69)) then
        tmp = t_1
    else if (y <= 5.2d+25) then
        tmp = (((a ** (t + (-1.0d0))) / exp(b)) * 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.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -5.8e+69) {
		tmp = t_1;
	} else if (y <= 5.2e+25) {
		tmp = ((Math.pow(a, (t + -1.0)) / Math.exp(b)) * x) / 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 <= -5.8e+69:
		tmp = t_1
	elif y <= 5.2e+25:
		tmp = ((math.pow(a, (t + -1.0)) / math.exp(b)) * x) / 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 <= -5.8e+69)
		tmp = t_1;
	elseif (y <= 5.2e+25)
		tmp = Float64(Float64(Float64((a ^ Float64(t + -1.0)) / exp(b)) * x) / 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 <= -5.8e+69)
		tmp = t_1;
	elseif (y <= 5.2e+25)
		tmp = (((a ^ (t + -1.0)) / exp(b)) * 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[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -5.8e+69], t$95$1, If[LessEqual[y, 5.2e+25], N[(N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7999999999999997e69 or 5.1999999999999997e25 < 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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -5.7999999999999997e69 < y < 5.1999999999999997e25

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 82.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{a}^{t}}{y}}{a}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{z}^{y}}{a}}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow a t) y)) a)))
   (if (<= t -2.4e+99)
     t_1
     (if (<= t 8e+79) (/ (* x (/ (/ (pow z y) a) (exp b))) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(a, t) / y)) / a;
	double tmp;
	if (t <= -2.4e+99) {
		tmp = t_1;
	} else if (t <= 8e+79) {
		tmp = (x * ((pow(z, y) / a) / exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((a ** t) / y)) / a
    if (t <= (-2.4d+99)) then
        tmp = t_1
    else if (t <= 8d+79) then
        tmp = (x * (((z ** y) / a) / exp(b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (Math.pow(a, t) / y)) / a;
	double tmp;
	if (t <= -2.4e+99) {
		tmp = t_1;
	} else if (t <= 8e+79) {
		tmp = (x * ((Math.pow(z, y) / a) / Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(a, t) / y)) / a
	tmp = 0
	if t <= -2.4e+99:
		tmp = t_1
	elif t <= 8e+79:
		tmp = (x * ((math.pow(z, y) / a) / math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((a ^ t) / y)) / a)
	tmp = 0.0
	if (t <= -2.4e+99)
		tmp = t_1;
	elseif (t <= 8e+79)
		tmp = Float64(Float64(x * Float64(Float64((z ^ y) / a) / exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((a ^ t) / y)) / a;
	tmp = 0.0;
	if (t <= -2.4e+99)
		tmp = t_1;
	elseif (t <= 8e+79)
		tmp = (x * (((z ^ y) / a) / exp(b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t, -2.4e+99], t$95$1, If[LessEqual[t, 8e+79], N[(N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4000000000000001e99 or 7.99999999999999974e79 < t

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]

   if -2.4000000000000001e99 < t < 7.99999999999999974e79

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 55.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot y}\\ t_2 := \frac{\frac{x}{a}}{y \cdot e^{b}}\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{x}{y} + b \cdot \left(b \cdot \left(0.5 \cdot \frac{x}{y} + \frac{\left(b \cdot -0.16666666666666666\right) \cdot x}{y}\right) - \frac{x}{y}\right)}{a}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-288}:\\ \;\;\;\;t\_1 + b \cdot \left(b \cdot \left(b \cdot \left(t\_1 \cdot -0.16666666666666666 + \left(0.5 \cdot \frac{t\_1}{b} - \frac{\frac{\frac{x}{a \cdot b}}{b}}{y}\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-207}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \frac{b \cdot b}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a y))) (t_2 (/ (/ x a) (* y (exp b)))))
   (if (<= b -7.5e+83)
     (/
      (+
       (/ x y)
       (*
        b
        (-
         (* b (+ (* 0.5 (/ x y)) (/ (* (* b -0.16666666666666666) x) y)))
         (/ x y))))
      a)
     (if (<= b -8.2e-20)
       t_2
       (if (<= b -2.6e-288)
         (+
          t_1
          (*
           b
           (*
            b
            (*
             b
             (+
              (* t_1 -0.16666666666666666)
              (- (* 0.5 (/ t_1 b)) (/ (/ (/ x (* a b)) b) y)))))))
         (if (<= b 3.6e-207) (/ (* 0.5 (* x (/ (* b b) a))) y) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * y);
	double t_2 = (x / a) / (y * exp(b));
	double tmp;
	if (b <= -7.5e+83) {
		tmp = ((x / y) + (b * ((b * ((0.5 * (x / y)) + (((b * -0.16666666666666666) * x) / y))) - (x / y)))) / a;
	} else if (b <= -8.2e-20) {
		tmp = t_2;
	} else if (b <= -2.6e-288) {
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))));
	} else if (b <= 3.6e-207) {
		tmp = (0.5 * (x * ((b * b) / a))) / 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 = x / (a * y)
    t_2 = (x / a) / (y * exp(b))
    if (b <= (-7.5d+83)) then
        tmp = ((x / y) + (b * ((b * ((0.5d0 * (x / y)) + (((b * (-0.16666666666666666d0)) * x) / y))) - (x / y)))) / a
    else if (b <= (-8.2d-20)) then
        tmp = t_2
    else if (b <= (-2.6d-288)) then
        tmp = t_1 + (b * (b * (b * ((t_1 * (-0.16666666666666666d0)) + ((0.5d0 * (t_1 / b)) - (((x / (a * b)) / b) / y))))))
    else if (b <= 3.6d-207) then
        tmp = (0.5d0 * (x * ((b * b) / a))) / 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 = x / (a * y);
	double t_2 = (x / a) / (y * Math.exp(b));
	double tmp;
	if (b <= -7.5e+83) {
		tmp = ((x / y) + (b * ((b * ((0.5 * (x / y)) + (((b * -0.16666666666666666) * x) / y))) - (x / y)))) / a;
	} else if (b <= -8.2e-20) {
		tmp = t_2;
	} else if (b <= -2.6e-288) {
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))));
	} else if (b <= 3.6e-207) {
		tmp = (0.5 * (x * ((b * b) / a))) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * y)
	t_2 = (x / a) / (y * math.exp(b))
	tmp = 0
	if b <= -7.5e+83:
		tmp = ((x / y) + (b * ((b * ((0.5 * (x / y)) + (((b * -0.16666666666666666) * x) / y))) - (x / y)))) / a
	elif b <= -8.2e-20:
		tmp = t_2
	elif b <= -2.6e-288:
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))))
	elif b <= 3.6e-207:
		tmp = (0.5 * (x * ((b * b) / a))) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * y))
	t_2 = Float64(Float64(x / a) / Float64(y * exp(b)))
	tmp = 0.0
	if (b <= -7.5e+83)
		tmp = Float64(Float64(Float64(x / y) + Float64(b * Float64(Float64(b * Float64(Float64(0.5 * Float64(x / y)) + Float64(Float64(Float64(b * -0.16666666666666666) * x) / y))) - Float64(x / y)))) / a);
	elseif (b <= -8.2e-20)
		tmp = t_2;
	elseif (b <= -2.6e-288)
		tmp = Float64(t_1 + Float64(b * Float64(b * Float64(b * Float64(Float64(t_1 * -0.16666666666666666) + Float64(Float64(0.5 * Float64(t_1 / b)) - Float64(Float64(Float64(x / Float64(a * b)) / b) / y)))))));
	elseif (b <= 3.6e-207)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(Float64(b * b) / a))) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * y);
	t_2 = (x / a) / (y * exp(b));
	tmp = 0.0;
	if (b <= -7.5e+83)
		tmp = ((x / y) + (b * ((b * ((0.5 * (x / y)) + (((b * -0.16666666666666666) * x) / y))) - (x / y)))) / a;
	elseif (b <= -8.2e-20)
		tmp = t_2;
	elseif (b <= -2.6e-288)
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))));
	elseif (b <= 3.6e-207)
		tmp = (0.5 * (x * ((b * b) / a))) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e+83], N[(N[(N[(x / y), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(0.5 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * -0.16666666666666666), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -8.2e-20], t$95$2, If[LessEqual[b, -2.6e-288], N[(t$95$1 + N[(b * N[(b * N[(b * N[(N[(t$95$1 * -0.16666666666666666), $MachinePrecision] + N[(N[(0.5 * N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e-207], N[(N[(0.5 * N[(x * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.49999999999999989e83

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if -7.49999999999999989e83 < b < -8.2000000000000002e-20 or 3.5999999999999997e-207 < b

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -8.2000000000000002e-20 < b < -2.59999999999999989e-288

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if -2.59999999999999989e-288 < b < 3.5999999999999997e-207

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 73.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{1 + b}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -5.7e+69)
     t_1
     (if (<= y -7e-84)
       (/ (/ x y) (/ (+ 1.0 b) (pow a (+ t -1.0))))
       (if (<= y 5.8e+36) (/ (/ x (* a (exp b))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -5.7e+69) {
		tmp = t_1;
	} else if (y <= -7e-84) {
		tmp = (x / y) / ((1.0 + b) / pow(a, (t + -1.0)));
	} else if (y <= 5.8e+36) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * (z ** y)) / a) / y
    if (y <= (-5.7d+69)) then
        tmp = t_1
    else if (y <= (-7d-84)) then
        tmp = (x / y) / ((1.0d0 + b) / (a ** (t + (-1.0d0))))
    else if (y <= 5.8d+36) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -5.7e+69) {
		tmp = t_1;
	} else if (y <= -7e-84) {
		tmp = (x / y) / ((1.0 + b) / Math.pow(a, (t + -1.0)));
	} else if (y <= 5.8e+36) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -5.7e+69:
		tmp = t_1
	elif y <= -7e-84:
		tmp = (x / y) / ((1.0 + b) / math.pow(a, (t + -1.0)))
	elif y <= 5.8e+36:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -5.7e+69)
		tmp = t_1;
	elseif (y <= -7e-84)
		tmp = Float64(Float64(x / y) / Float64(Float64(1.0 + b) / (a ^ Float64(t + -1.0))));
	elseif (y <= 5.8e+36)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -5.7e+69)
		tmp = t_1;
	elseif (y <= -7e-84)
		tmp = (x / y) / ((1.0 + b) / (a ^ (t + -1.0)));
	elseif (y <= 5.8e+36)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -5.7e+69], t$95$1, If[LessEqual[y, -7e-84], N[(N[(x / y), $MachinePrecision] / N[(N[(1.0 + b), $MachinePrecision] / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+36], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7e69 or 5.8e36 < 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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -5.7e69 < y < -7.0000000000000002e-84

   1. Initial program 98.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -7.0000000000000002e-84 < y < 5.8e36

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 74.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{y}}{a}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -5.7e+69)
     t_1
     (if (<= y -6e-84)
       (/ (* x (/ (pow a t) y)) a)
       (if (<= y 2.65e+36) (/ (/ x (* a (exp b))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -5.7e+69) {
		tmp = t_1;
	} else if (y <= -6e-84) {
		tmp = (x * (pow(a, t) / y)) / a;
	} else if (y <= 2.65e+36) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * (z ** y)) / a) / y
    if (y <= (-5.7d+69)) then
        tmp = t_1
    else if (y <= (-6d-84)) then
        tmp = (x * ((a ** t) / y)) / a
    else if (y <= 2.65d+36) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -5.7e+69) {
		tmp = t_1;
	} else if (y <= -6e-84) {
		tmp = (x * (Math.pow(a, t) / y)) / a;
	} else if (y <= 2.65e+36) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -5.7e+69:
		tmp = t_1
	elif y <= -6e-84:
		tmp = (x * (math.pow(a, t) / y)) / a
	elif y <= 2.65e+36:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -5.7e+69)
		tmp = t_1;
	elseif (y <= -6e-84)
		tmp = Float64(Float64(x * Float64((a ^ t) / y)) / a);
	elseif (y <= 2.65e+36)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -5.7e+69)
		tmp = t_1;
	elseif (y <= -6e-84)
		tmp = (x * ((a ^ t) / y)) / a;
	elseif (y <= 2.65e+36)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -5.7e+69], t$95$1, If[LessEqual[y, -6e-84], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 2.65e+36], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7e69 or 2.65e36 < 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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -5.7e69 < y < -6.0000000000000002e-84

   1. Initial program 98.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]

   if -6.0000000000000002e-84 < y < 2.65e36

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 73.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{if}\;b \leq -46:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-213}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{y}}{a}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (* a (exp b))) y)))
   (if (<= b -46.0)
     t_1
     (if (<= b -9.2e-213)
       (/ (* x (/ (pow a t) y)) a)
       (if (<= b 6.5e+89) (/ (* x (pow z y)) (* a y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a * exp(b))) / y;
	double tmp;
	if (b <= -46.0) {
		tmp = t_1;
	} else if (b <= -9.2e-213) {
		tmp = (x * (pow(a, t) / y)) / a;
	} else if (b <= 6.5e+89) {
		tmp = (x * pow(z, y)) / (a * 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 / (a * exp(b))) / y
    if (b <= (-46.0d0)) then
        tmp = t_1
    else if (b <= (-9.2d-213)) then
        tmp = (x * ((a ** t) / y)) / a
    else if (b <= 6.5d+89) then
        tmp = (x * (z ** y)) / (a * 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 / (a * Math.exp(b))) / y;
	double tmp;
	if (b <= -46.0) {
		tmp = t_1;
	} else if (b <= -9.2e-213) {
		tmp = (x * (Math.pow(a, t) / y)) / a;
	} else if (b <= 6.5e+89) {
		tmp = (x * Math.pow(z, y)) / (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a * math.exp(b))) / y
	tmp = 0
	if b <= -46.0:
		tmp = t_1
	elif b <= -9.2e-213:
		tmp = (x * (math.pow(a, t) / y)) / a
	elif b <= 6.5e+89:
		tmp = (x * math.pow(z, y)) / (a * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a * exp(b))) / y)
	tmp = 0.0
	if (b <= -46.0)
		tmp = t_1;
	elseif (b <= -9.2e-213)
		tmp = Float64(Float64(x * Float64((a ^ t) / y)) / a);
	elseif (b <= 6.5e+89)
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (a * exp(b))) / y;
	tmp = 0.0;
	if (b <= -46.0)
		tmp = t_1;
	elseif (b <= -9.2e-213)
		tmp = (x * ((a ^ t) / y)) / a;
	elseif (b <= 6.5e+89)
		tmp = (x * (z ^ y)) / (a * 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[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -46.0], t$95$1, If[LessEqual[b, -9.2e-213], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 6.5e+89], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -46 or 6.4999999999999996e89 < 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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -46 < b < -9.20000000000000011e-213

   1. Initial program 98.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]

   if -9.20000000000000011e-213 < b < 6.4999999999999996e89

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 60.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot y}\\ t_2 := \frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-292}:\\ \;\;\;\;t\_1 + b \cdot \left(b \cdot \left(b \cdot \left(t\_1 \cdot -0.16666666666666666 + \left(0.5 \cdot \frac{t\_1}{b} - \frac{\frac{\frac{x}{a \cdot b}}{b}}{y}\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-207}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \frac{b \cdot b}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a y))) (t_2 (/ (/ x (* a (exp b))) y)))
   (if (<= b -4.1e-13)
     t_2
     (if (<= b -1.9e-292)
       (+
        t_1
        (*
         b
         (*
          b
          (*
           b
           (+
            (* t_1 -0.16666666666666666)
            (- (* 0.5 (/ t_1 b)) (/ (/ (/ x (* a b)) b) y)))))))
       (if (<= b 2.8e-207) (/ (* 0.5 (* x (/ (* b b) a))) y) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * y);
	double t_2 = (x / (a * exp(b))) / y;
	double tmp;
	if (b <= -4.1e-13) {
		tmp = t_2;
	} else if (b <= -1.9e-292) {
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))));
	} else if (b <= 2.8e-207) {
		tmp = (0.5 * (x * ((b * b) / a))) / 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 = x / (a * y)
    t_2 = (x / (a * exp(b))) / y
    if (b <= (-4.1d-13)) then
        tmp = t_2
    else if (b <= (-1.9d-292)) then
        tmp = t_1 + (b * (b * (b * ((t_1 * (-0.16666666666666666d0)) + ((0.5d0 * (t_1 / b)) - (((x / (a * b)) / b) / y))))))
    else if (b <= 2.8d-207) then
        tmp = (0.5d0 * (x * ((b * b) / a))) / 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 = x / (a * y);
	double t_2 = (x / (a * Math.exp(b))) / y;
	double tmp;
	if (b <= -4.1e-13) {
		tmp = t_2;
	} else if (b <= -1.9e-292) {
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))));
	} else if (b <= 2.8e-207) {
		tmp = (0.5 * (x * ((b * b) / a))) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * y)
	t_2 = (x / (a * math.exp(b))) / y
	tmp = 0
	if b <= -4.1e-13:
		tmp = t_2
	elif b <= -1.9e-292:
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))))
	elif b <= 2.8e-207:
		tmp = (0.5 * (x * ((b * b) / a))) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * y))
	t_2 = Float64(Float64(x / Float64(a * exp(b))) / y)
	tmp = 0.0
	if (b <= -4.1e-13)
		tmp = t_2;
	elseif (b <= -1.9e-292)
		tmp = Float64(t_1 + Float64(b * Float64(b * Float64(b * Float64(Float64(t_1 * -0.16666666666666666) + Float64(Float64(0.5 * Float64(t_1 / b)) - Float64(Float64(Float64(x / Float64(a * b)) / b) / y)))))));
	elseif (b <= 2.8e-207)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(Float64(b * b) / a))) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * y);
	t_2 = (x / (a * exp(b))) / y;
	tmp = 0.0;
	if (b <= -4.1e-13)
		tmp = t_2;
	elseif (b <= -1.9e-292)
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))));
	elseif (b <= 2.8e-207)
		tmp = (0.5 * (x * ((b * b) / a))) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -4.1e-13], t$95$2, If[LessEqual[b, -1.9e-292], N[(t$95$1 + N[(b * N[(b * N[(b * N[(N[(t$95$1 * -0.16666666666666666), $MachinePrecision] + N[(N[(0.5 * N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e-207], N[(N[(0.5 * N[(x * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.1000000000000002e-13 or 2.79999999999999993e-207 < b

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -4.1000000000000002e-13 < b < -1.9000000000000001e-292

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if -1.9000000000000001e-292 < b < 2.79999999999999993e-207

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 55.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot y}\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{\frac{x}{y}}{a \cdot e^{b}}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-288}:\\ \;\;\;\;t\_1 + b \cdot \left(b \cdot \left(b \cdot \left(t\_1 \cdot -0.16666666666666666 + \left(0.5 \cdot \frac{t\_1}{b} - \frac{\frac{\frac{x}{a \cdot b}}{b}}{y}\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-207}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \frac{b \cdot b}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a y))))
   (if (<= b -6.8e-191)
     (/ (/ x y) (* a (exp b)))
     (if (<= b -5e-288)
       (+
        t_1
        (*
         b
         (*
          b
          (*
           b
           (+
            (* t_1 -0.16666666666666666)
            (- (* 0.5 (/ t_1 b)) (/ (/ (/ x (* a b)) b) y)))))))
       (if (<= b 1.2e-207)
         (/ (* 0.5 (* x (/ (* b b) a))) y)
         (/ (/ x a) (* y (exp b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * y);
	double tmp;
	if (b <= -6.8e-191) {
		tmp = (x / y) / (a * exp(b));
	} else if (b <= -5e-288) {
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))));
	} else if (b <= 1.2e-207) {
		tmp = (0.5 * (x * ((b * b) / a))) / y;
	} else {
		tmp = (x / a) / (y * exp(b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a * y)
    if (b <= (-6.8d-191)) then
        tmp = (x / y) / (a * exp(b))
    else if (b <= (-5d-288)) then
        tmp = t_1 + (b * (b * (b * ((t_1 * (-0.16666666666666666d0)) + ((0.5d0 * (t_1 / b)) - (((x / (a * b)) / b) / y))))))
    else if (b <= 1.2d-207) then
        tmp = (0.5d0 * (x * ((b * b) / a))) / y
    else
        tmp = (x / a) / (y * exp(b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * y);
	double tmp;
	if (b <= -6.8e-191) {
		tmp = (x / y) / (a * Math.exp(b));
	} else if (b <= -5e-288) {
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))));
	} else if (b <= 1.2e-207) {
		tmp = (0.5 * (x * ((b * b) / a))) / y;
	} else {
		tmp = (x / a) / (y * Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * y)
	tmp = 0
	if b <= -6.8e-191:
		tmp = (x / y) / (a * math.exp(b))
	elif b <= -5e-288:
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))))
	elif b <= 1.2e-207:
		tmp = (0.5 * (x * ((b * b) / a))) / y
	else:
		tmp = (x / a) / (y * math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * y))
	tmp = 0.0
	if (b <= -6.8e-191)
		tmp = Float64(Float64(x / y) / Float64(a * exp(b)));
	elseif (b <= -5e-288)
		tmp = Float64(t_1 + Float64(b * Float64(b * Float64(b * Float64(Float64(t_1 * -0.16666666666666666) + Float64(Float64(0.5 * Float64(t_1 / b)) - Float64(Float64(Float64(x / Float64(a * b)) / b) / y)))))));
	elseif (b <= 1.2e-207)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(Float64(b * b) / a))) / y);
	else
		tmp = Float64(Float64(x / a) / Float64(y * exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * y);
	tmp = 0.0;
	if (b <= -6.8e-191)
		tmp = (x / y) / (a * exp(b));
	elseif (b <= -5e-288)
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))));
	elseif (b <= 1.2e-207)
		tmp = (0.5 * (x * ((b * b) / a))) / y;
	else
		tmp = (x / a) / (y * exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e-191], N[(N[(x / y), $MachinePrecision] / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5e-288], N[(t$95$1 + N[(b * N[(b * N[(b * N[(N[(t$95$1 * -0.16666666666666666), $MachinePrecision] + N[(N[(0.5 * N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e-207], N[(N[(0.5 * N[(x * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.79999999999999988e-191

   1. Initial program 99.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -6.79999999999999988e-191 < b < -5.00000000000000011e-288

   1. Initial program 94.2%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if -5.00000000000000011e-288 < b < 1.19999999999999994e-207

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if 1.19999999999999994e-207 < b

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 76.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{if}\;b \leq -2050:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 0.00019:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (* a (exp b))) y)))
   (if (<= b -2050.0)
     t_1
     (if (<= b 0.00019) (/ (* x (/ (pow a t) y)) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a * exp(b))) / y;
	double tmp;
	if (b <= -2050.0) {
		tmp = t_1;
	} else if (b <= 0.00019) {
		tmp = (x * (pow(a, t) / 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 / (a * exp(b))) / y
    if (b <= (-2050.0d0)) then
        tmp = t_1
    else if (b <= 0.00019d0) then
        tmp = (x * ((a ** t) / 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 / (a * Math.exp(b))) / y;
	double tmp;
	if (b <= -2050.0) {
		tmp = t_1;
	} else if (b <= 0.00019) {
		tmp = (x * (Math.pow(a, t) / y)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a * math.exp(b))) / y
	tmp = 0
	if b <= -2050.0:
		tmp = t_1
	elif b <= 0.00019:
		tmp = (x * (math.pow(a, t) / y)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a * exp(b))) / y)
	tmp = 0.0
	if (b <= -2050.0)
		tmp = t_1;
	elseif (b <= 0.00019)
		tmp = Float64(Float64(x * Float64((a ^ t) / y)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (a * exp(b))) / y;
	tmp = 0.0;
	if (b <= -2050.0)
		tmp = t_1;
	elseif (b <= 0.00019)
		tmp = (x * ((a ^ t) / 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[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -2050.0], t$95$1, If[LessEqual[b, 0.00019], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2050 or 1.9000000000000001e-4 < b

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -2050 < b < 1.9000000000000001e-4

   1. Initial program 97.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 51.5% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot y}\\ t_2 := \frac{0.5 \cdot \left(x \cdot \frac{b \cdot b}{a}\right)}{y}\\ \mathbf{if}\;b \leq -2.52 \cdot 10^{+203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-291}:\\ \;\;\;\;t\_1 + b \cdot \left(b \cdot \left(b \cdot \left(t\_1 \cdot -0.16666666666666666 + \left(0.5 \cdot \frac{t\_1}{b} - \frac{\frac{\frac{x}{a \cdot b}}{b}}{y}\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-208}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a y))) (t_2 (/ (* 0.5 (* x (/ (* b b) a))) y)))
   (if (<= b -2.52e+203)
     t_2
     (if (<= b -2.7e-291)
       (+
        t_1
        (*
         b
         (*
          b
          (*
           b
           (+
            (* t_1 -0.16666666666666666)
            (- (* 0.5 (/ t_1 b)) (/ (/ (/ x (* a b)) b) y)))))))
       (if (<= b 3.1e-208)
         t_2
         (/
          (/ x a)
          (*
           y
           (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* 0.16666666666666666 b)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * y);
	double t_2 = (0.5 * (x * ((b * b) / a))) / y;
	double tmp;
	if (b <= -2.52e+203) {
		tmp = t_2;
	} else if (b <= -2.7e-291) {
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))));
	} else if (b <= 3.1e-208) {
		tmp = t_2;
	} else {
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (b * (0.5 + (0.16666666666666666 * b)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (a * y)
    t_2 = (0.5d0 * (x * ((b * b) / a))) / y
    if (b <= (-2.52d+203)) then
        tmp = t_2
    else if (b <= (-2.7d-291)) then
        tmp = t_1 + (b * (b * (b * ((t_1 * (-0.16666666666666666d0)) + ((0.5d0 * (t_1 / b)) - (((x / (a * b)) / b) / y))))))
    else if (b <= 3.1d-208) then
        tmp = t_2
    else
        tmp = (x / a) / (y * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (0.16666666666666666d0 * b)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * y);
	double t_2 = (0.5 * (x * ((b * b) / a))) / y;
	double tmp;
	if (b <= -2.52e+203) {
		tmp = t_2;
	} else if (b <= -2.7e-291) {
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))));
	} else if (b <= 3.1e-208) {
		tmp = t_2;
	} else {
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (b * (0.5 + (0.16666666666666666 * b)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * y)
	t_2 = (0.5 * (x * ((b * b) / a))) / y
	tmp = 0
	if b <= -2.52e+203:
		tmp = t_2
	elif b <= -2.7e-291:
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))))
	elif b <= 3.1e-208:
		tmp = t_2
	else:
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (b * (0.5 + (0.16666666666666666 * b)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * y))
	t_2 = Float64(Float64(0.5 * Float64(x * Float64(Float64(b * b) / a))) / y)
	tmp = 0.0
	if (b <= -2.52e+203)
		tmp = t_2;
	elseif (b <= -2.7e-291)
		tmp = Float64(t_1 + Float64(b * Float64(b * Float64(b * Float64(Float64(t_1 * -0.16666666666666666) + Float64(Float64(0.5 * Float64(t_1 / b)) - Float64(Float64(Float64(x / Float64(a * b)) / b) / y)))))));
	elseif (b <= 3.1e-208)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / a) / Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(0.16666666666666666 * b))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * y);
	t_2 = (0.5 * (x * ((b * b) / a))) / y;
	tmp = 0.0;
	if (b <= -2.52e+203)
		tmp = t_2;
	elseif (b <= -2.7e-291)
		tmp = t_1 + (b * (b * (b * ((t_1 * -0.16666666666666666) + ((0.5 * (t_1 / b)) - (((x / (a * b)) / b) / y))))));
	elseif (b <= 3.1e-208)
		tmp = t_2;
	else
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (b * (0.5 + (0.16666666666666666 * b)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(0.5 * N[(x * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -2.52e+203], t$95$2, If[LessEqual[b, -2.7e-291], N[(t$95$1 + N[(b * N[(b * N[(b * N[(N[(t$95$1 * -0.16666666666666666), $MachinePrecision] + N[(N[(0.5 * N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-208], t$95$2, N[(N[(x / a), $MachinePrecision] / N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(0.16666666666666666 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.52000000000000001e203 or -2.69999999999999992e-291 < b < 3.0999999999999998e-208

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if -2.52000000000000001e203 < b < -2.69999999999999992e-291

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if 3.0999999999999998e-208 < b

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 51.0% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-288}:\\ \;\;\;\;\frac{\frac{x}{y} + b \cdot \left(b \cdot \left(0.5 \cdot \frac{x}{y} + \frac{\left(b \cdot -0.16666666666666666\right) \cdot x}{y}\right) - \frac{x}{y}\right)}{a}\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-207}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \frac{b \cdot b}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3e-288)
   (/
    (+
     (/ x y)
     (*
      b
      (-
       (* b (+ (* 0.5 (/ x y)) (/ (* (* b -0.16666666666666666) x) y)))
       (/ x y))))
    a)
   (if (<= b 2.35e-207)
     (/ (* 0.5 (* x (/ (* b b) a))) y)
     (/
      (/ x a)
      (* y (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* 0.16666666666666666 b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-288) {
		tmp = ((x / y) + (b * ((b * ((0.5 * (x / y)) + (((b * -0.16666666666666666) * x) / y))) - (x / y)))) / a;
	} else if (b <= 2.35e-207) {
		tmp = (0.5 * (x * ((b * b) / a))) / y;
	} else {
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (b * (0.5 + (0.16666666666666666 * b)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3d-288)) then
        tmp = ((x / y) + (b * ((b * ((0.5d0 * (x / y)) + (((b * (-0.16666666666666666d0)) * x) / y))) - (x / y)))) / a
    else if (b <= 2.35d-207) then
        tmp = (0.5d0 * (x * ((b * b) / a))) / y
    else
        tmp = (x / a) / (y * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (0.16666666666666666d0 * b)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-288) {
		tmp = ((x / y) + (b * ((b * ((0.5 * (x / y)) + (((b * -0.16666666666666666) * x) / y))) - (x / y)))) / a;
	} else if (b <= 2.35e-207) {
		tmp = (0.5 * (x * ((b * b) / a))) / y;
	} else {
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (b * (0.5 + (0.16666666666666666 * b)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3e-288:
		tmp = ((x / y) + (b * ((b * ((0.5 * (x / y)) + (((b * -0.16666666666666666) * x) / y))) - (x / y)))) / a
	elif b <= 2.35e-207:
		tmp = (0.5 * (x * ((b * b) / a))) / y
	else:
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (b * (0.5 + (0.16666666666666666 * b)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3e-288)
		tmp = Float64(Float64(Float64(x / y) + Float64(b * Float64(Float64(b * Float64(Float64(0.5 * Float64(x / y)) + Float64(Float64(Float64(b * -0.16666666666666666) * x) / y))) - Float64(x / y)))) / a);
	elseif (b <= 2.35e-207)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(Float64(b * b) / a))) / y);
	else
		tmp = Float64(Float64(x / a) / Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(0.16666666666666666 * b))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3e-288)
		tmp = ((x / y) + (b * ((b * ((0.5 * (x / y)) + (((b * -0.16666666666666666) * x) / y))) - (x / y)))) / a;
	elseif (b <= 2.35e-207)
		tmp = (0.5 * (x * ((b * b) / a))) / y;
	else
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (b * (0.5 + (0.16666666666666666 * b)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3e-288], N[(N[(N[(x / y), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(0.5 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * -0.16666666666666666), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 2.35e-207], N[(N[(0.5 * N[(x * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(0.16666666666666666 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.99999999999999999e-288

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if -2.99999999999999999e-288 < b < 2.35000000000000014e-207

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if 2.35000000000000014e-207 < b

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 44.9% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{0.5 \cdot \left(x \cdot \frac{b \cdot b}{a}\right)}{y}\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-290}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{b + 1} \cdot \frac{1}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* 0.5 (* x (/ (* b b) a))) y)))
   (if (<= b -1.2e+86)
     t_1
     (if (<= b -4.4e-290)
       (* (/ 1.0 a) (/ x y))
       (if (<= b 5.8e-208) t_1 (/ (* (/ x (+ b 1.0)) (/ 1.0 y)) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.5 * (x * ((b * b) / a))) / y;
	double tmp;
	if (b <= -1.2e+86) {
		tmp = t_1;
	} else if (b <= -4.4e-290) {
		tmp = (1.0 / a) * (x / y);
	} else if (b <= 5.8e-208) {
		tmp = t_1;
	} else {
		tmp = ((x / (b + 1.0)) * (1.0 / y)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (0.5d0 * (x * ((b * b) / a))) / y
    if (b <= (-1.2d+86)) then
        tmp = t_1
    else if (b <= (-4.4d-290)) then
        tmp = (1.0d0 / a) * (x / y)
    else if (b <= 5.8d-208) then
        tmp = t_1
    else
        tmp = ((x / (b + 1.0d0)) * (1.0d0 / y)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.5 * (x * ((b * b) / a))) / y;
	double tmp;
	if (b <= -1.2e+86) {
		tmp = t_1;
	} else if (b <= -4.4e-290) {
		tmp = (1.0 / a) * (x / y);
	} else if (b <= 5.8e-208) {
		tmp = t_1;
	} else {
		tmp = ((x / (b + 1.0)) * (1.0 / y)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (0.5 * (x * ((b * b) / a))) / y
	tmp = 0
	if b <= -1.2e+86:
		tmp = t_1
	elif b <= -4.4e-290:
		tmp = (1.0 / a) * (x / y)
	elif b <= 5.8e-208:
		tmp = t_1
	else:
		tmp = ((x / (b + 1.0)) * (1.0 / y)) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(0.5 * Float64(x * Float64(Float64(b * b) / a))) / y)
	tmp = 0.0
	if (b <= -1.2e+86)
		tmp = t_1;
	elseif (b <= -4.4e-290)
		tmp = Float64(Float64(1.0 / a) * Float64(x / y));
	elseif (b <= 5.8e-208)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(x / Float64(b + 1.0)) * Float64(1.0 / y)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (0.5 * (x * ((b * b) / a))) / y;
	tmp = 0.0;
	if (b <= -1.2e+86)
		tmp = t_1;
	elseif (b <= -4.4e-290)
		tmp = (1.0 / a) * (x / y);
	elseif (b <= 5.8e-208)
		tmp = t_1;
	else
		tmp = ((x / (b + 1.0)) * (1.0 / y)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(0.5 * N[(x * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.2e+86], t$95$1, If[LessEqual[b, -4.4e-290], N[(N[(1.0 / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e-208], t$95$1, N[(N[(N[(x / N[(b + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.2e86 or -4.4000000000000002e-290 < b < 5.7999999999999999e-208

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if -1.2e86 < b < -4.4000000000000002e-290

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   13. Applied egg-rr 0

       \[\leadsto expr\]

   if 5.7999999999999999e-208 < b

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   13. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 44.7% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{0.5 \cdot \left(x \cdot \frac{b \cdot b}{a}\right)}{y}\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-292}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(b + 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* 0.5 (* x (/ (* b b) a))) y)))
   (if (<= b -7.8e+86)
     t_1
     (if (<= b -1.85e-292)
       (* (/ 1.0 a) (/ x y))
       (if (<= b 5.7e-208) t_1 (/ x (* y (* a (+ b 1.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.5 * (x * ((b * b) / a))) / y;
	double tmp;
	if (b <= -7.8e+86) {
		tmp = t_1;
	} else if (b <= -1.85e-292) {
		tmp = (1.0 / a) * (x / y);
	} else if (b <= 5.7e-208) {
		tmp = t_1;
	} else {
		tmp = x / (y * (a * (b + 1.0)));
	}
	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 = (0.5d0 * (x * ((b * b) / a))) / y
    if (b <= (-7.8d+86)) then
        tmp = t_1
    else if (b <= (-1.85d-292)) then
        tmp = (1.0d0 / a) * (x / y)
    else if (b <= 5.7d-208) then
        tmp = t_1
    else
        tmp = x / (y * (a * (b + 1.0d0)))
    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 = (0.5 * (x * ((b * b) / a))) / y;
	double tmp;
	if (b <= -7.8e+86) {
		tmp = t_1;
	} else if (b <= -1.85e-292) {
		tmp = (1.0 / a) * (x / y);
	} else if (b <= 5.7e-208) {
		tmp = t_1;
	} else {
		tmp = x / (y * (a * (b + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (0.5 * (x * ((b * b) / a))) / y
	tmp = 0
	if b <= -7.8e+86:
		tmp = t_1
	elif b <= -1.85e-292:
		tmp = (1.0 / a) * (x / y)
	elif b <= 5.7e-208:
		tmp = t_1
	else:
		tmp = x / (y * (a * (b + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(0.5 * Float64(x * Float64(Float64(b * b) / a))) / y)
	tmp = 0.0
	if (b <= -7.8e+86)
		tmp = t_1;
	elseif (b <= -1.85e-292)
		tmp = Float64(Float64(1.0 / a) * Float64(x / y));
	elseif (b <= 5.7e-208)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(b + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (0.5 * (x * ((b * b) / a))) / y;
	tmp = 0.0;
	if (b <= -7.8e+86)
		tmp = t_1;
	elseif (b <= -1.85e-292)
		tmp = (1.0 / a) * (x / y);
	elseif (b <= 5.7e-208)
		tmp = t_1;
	else
		tmp = x / (y * (a * (b + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(0.5 * N[(x * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -7.8e+86], t$95$1, If[LessEqual[b, -1.85e-292], N[(N[(1.0 / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.7e-208], t$95$1, N[(x / N[(y * N[(a * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.8000000000000004e86 or -1.84999999999999998e-292 < b < 5.7000000000000004e-208

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if -7.8000000000000004e86 < b < -1.84999999999999998e-292

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   13. Applied egg-rr 0

       \[\leadsto expr\]

   if 5.7000000000000004e-208 < b

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   13. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 48.0% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 7.4 \cdot 10^{-208}:\\ \;\;\;\;\frac{-0.16666666666666666 \cdot \left(x \cdot \left(b \cdot \frac{b \cdot b}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+128}:\\ \;\;\;\;\frac{\frac{x}{b + 1} \cdot \frac{1}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y \cdot \left(1 + b \cdot \left(1 + 0.5 \cdot b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 7.4e-208)
   (/ (* -0.16666666666666666 (* x (* b (/ (* b b) a)))) y)
   (if (<= b 6.4e+128)
     (/ (* (/ x (+ b 1.0)) (/ 1.0 y)) a)
     (/ (/ x a) (* y (+ 1.0 (* b (+ 1.0 (* 0.5 b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.4e-208) {
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y;
	} else if (b <= 6.4e+128) {
		tmp = ((x / (b + 1.0)) * (1.0 / y)) / a;
	} else {
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (0.5 * b)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 7.4d-208) then
        tmp = ((-0.16666666666666666d0) * (x * (b * ((b * b) / a)))) / y
    else if (b <= 6.4d+128) then
        tmp = ((x / (b + 1.0d0)) * (1.0d0 / y)) / a
    else
        tmp = (x / a) / (y * (1.0d0 + (b * (1.0d0 + (0.5d0 * b)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.4e-208) {
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y;
	} else if (b <= 6.4e+128) {
		tmp = ((x / (b + 1.0)) * (1.0 / y)) / a;
	} else {
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (0.5 * b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 7.4e-208:
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y
	elif b <= 6.4e+128:
		tmp = ((x / (b + 1.0)) * (1.0 / y)) / a
	else:
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (0.5 * b)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 7.4e-208)
		tmp = Float64(Float64(-0.16666666666666666 * Float64(x * Float64(b * Float64(Float64(b * b) / a)))) / y);
	elseif (b <= 6.4e+128)
		tmp = Float64(Float64(Float64(x / Float64(b + 1.0)) * Float64(1.0 / y)) / a);
	else
		tmp = Float64(Float64(x / a) / Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(0.5 * b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 7.4e-208)
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y;
	elseif (b <= 6.4e+128)
		tmp = ((x / (b + 1.0)) * (1.0 / y)) / a;
	else
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (0.5 * b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 7.4e-208], N[(N[(-0.16666666666666666 * N[(x * N[(b * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6.4e+128], N[(N[(N[(x / N[(b + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / N[(y * N[(1.0 + N[(b * N[(1.0 + N[(0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 7.4000000000000004e-208

   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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if 7.4000000000000004e-208 < b < 6.39999999999999971e128

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   13. Applied egg-rr 0

       \[\leadsto expr\]

   if 6.39999999999999971e128 < 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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 49.6% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.5 \cdot 10^{-208}:\\ \;\;\;\;\frac{-0.16666666666666666 \cdot \left(x \cdot \left(b \cdot \frac{b \cdot b}{a}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.5e-208)
   (/ (* -0.16666666666666666 (* x (* b (/ (* b b) a)))) y)
   (/
    (/ x a)
    (* y (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* 0.16666666666666666 b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.5e-208) {
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y;
	} else {
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (b * (0.5 + (0.16666666666666666 * b)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.5d-208) then
        tmp = ((-0.16666666666666666d0) * (x * (b * ((b * b) / a)))) / y
    else
        tmp = (x / a) / (y * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (0.16666666666666666d0 * b)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.5e-208) {
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y;
	} else {
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (b * (0.5 + (0.16666666666666666 * b)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.5e-208:
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y
	else:
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (b * (0.5 + (0.16666666666666666 * b)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.5e-208)
		tmp = Float64(Float64(-0.16666666666666666 * Float64(x * Float64(b * Float64(Float64(b * b) / a)))) / y);
	else
		tmp = Float64(Float64(x / a) / Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(0.16666666666666666 * b))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.5e-208)
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y;
	else
		tmp = (x / a) / (y * (1.0 + (b * (1.0 + (b * (0.5 + (0.16666666666666666 * b)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.5e-208], N[(N[(-0.16666666666666666 * N[(x * N[(b * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(0.16666666666666666 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.49999999999999981e-208

   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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if 2.49999999999999981e-208 < b

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 49.8% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.4 \cdot 10^{-207}:\\ \;\;\;\;\frac{-0.16666666666666666 \cdot \left(x \cdot \left(b \cdot \frac{b \cdot b}{a}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + 0.5 \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.4e-207)
   (/ (* -0.16666666666666666 (* x (* b (/ (* b b) a)))) y)
   (/ (/ x (* a (+ 1.0 (* b (+ 1.0 (* 0.5 b)))))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.4e-207) {
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y;
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (0.5 * b)))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.4d-207) then
        tmp = ((-0.16666666666666666d0) * (x * (b * ((b * b) / a)))) / y
    else
        tmp = (x / (a * (1.0d0 + (b * (1.0d0 + (0.5d0 * b)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.4e-207) {
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y;
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (0.5 * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.4e-207:
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y
	else:
		tmp = (x / (a * (1.0 + (b * (1.0 + (0.5 * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.4e-207)
		tmp = Float64(Float64(-0.16666666666666666 * Float64(x * Float64(b * Float64(Float64(b * b) / a)))) / y);
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(0.5 * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.4e-207)
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y;
	else
		tmp = (x / (a * (1.0 + (b * (1.0 + (0.5 * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.4e-207], N[(N[(-0.16666666666666666 * N[(x * N[(b * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * N[(1.0 + N[(b * N[(1.0 + N[(0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.39999999999999999e-207

   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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if 3.39999999999999999e-207 < b

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 38.9% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.52 \cdot 10^{+181}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(-\left(b + -1\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+85}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(b + 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.52e+181)
   (/ (* (/ x a) (- (+ b -1.0))) y)
   (if (<= b 3.3e+85) (/ (/ x y) a) (/ x (* y (* a (+ b 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.52e+181) {
		tmp = ((x / a) * -(b + -1.0)) / y;
	} else if (b <= 3.3e+85) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * (a * (b + 1.0)));
	}
	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 <= (-1.52d+181)) then
        tmp = ((x / a) * -(b + (-1.0d0))) / y
    else if (b <= 3.3d+85) then
        tmp = (x / y) / a
    else
        tmp = x / (y * (a * (b + 1.0d0)))
    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 <= -1.52e+181) {
		tmp = ((x / a) * -(b + -1.0)) / y;
	} else if (b <= 3.3e+85) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * (a * (b + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.52e+181:
		tmp = ((x / a) * -(b + -1.0)) / y
	elif b <= 3.3e+85:
		tmp = (x / y) / a
	else:
		tmp = x / (y * (a * (b + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.52e+181)
		tmp = Float64(Float64(Float64(x / a) * Float64(-Float64(b + -1.0))) / y);
	elseif (b <= 3.3e+85)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(b + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.52e+181)
		tmp = ((x / a) * -(b + -1.0)) / y;
	elseif (b <= 3.3e+85)
		tmp = (x / y) / a;
	else
		tmp = x / (y * (a * (b + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.52e+181], N[(N[(N[(x / a), $MachinePrecision] * (-N[(b + -1.0), $MachinePrecision])), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.3e+85], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * N[(a * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.52e181

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around 0 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if -1.52e181 < b < 3.2999999999999999e85

   1. Initial program 98.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 3.2999999999999999e85 < 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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   13. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 44.4% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 7.5 \cdot 10^{-207}:\\ \;\;\;\;\frac{-0.16666666666666666 \cdot \left(x \cdot \left(b \cdot \frac{b \cdot b}{a}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{b + 1} \cdot \frac{1}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 7.5e-207)
   (/ (* -0.16666666666666666 (* x (* b (/ (* b b) a)))) y)
   (/ (* (/ x (+ b 1.0)) (/ 1.0 y)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.5e-207) {
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y;
	} else {
		tmp = ((x / (b + 1.0)) * (1.0 / y)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 7.5d-207) then
        tmp = ((-0.16666666666666666d0) * (x * (b * ((b * b) / a)))) / y
    else
        tmp = ((x / (b + 1.0d0)) * (1.0d0 / y)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.5e-207) {
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y;
	} else {
		tmp = ((x / (b + 1.0)) * (1.0 / y)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 7.5e-207:
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y
	else:
		tmp = ((x / (b + 1.0)) * (1.0 / y)) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 7.5e-207)
		tmp = Float64(Float64(-0.16666666666666666 * Float64(x * Float64(b * Float64(Float64(b * b) / a)))) / y);
	else
		tmp = Float64(Float64(Float64(x / Float64(b + 1.0)) * Float64(1.0 / y)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 7.5e-207)
		tmp = (-0.16666666666666666 * (x * (b * ((b * b) / a)))) / y;
	else
		tmp = ((x / (b + 1.0)) * (1.0 / y)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 7.5e-207], N[(N[(-0.16666666666666666 * N[(x * N[(b * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x / N[(b + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 7.5000000000000006e-207

   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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if 7.5000000000000006e-207 < b

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   13. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 36.1% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.76 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(b + 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.76e+84) (/ (/ x y) a) (/ x (* y (* a (+ b 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.76e+84) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * (a * (b + 1.0)));
	}
	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 <= 1.76d+84) then
        tmp = (x / y) / a
    else
        tmp = x / (y * (a * (b + 1.0d0)))
    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 <= 1.76e+84) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * (a * (b + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.76e+84:
		tmp = (x / y) / a
	else:
		tmp = x / (y * (a * (b + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.76e+84)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(b + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.76e+84)
		tmp = (x / y) / a;
	else
		tmp = x / (y * (a * (b + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.76e+84], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * N[(a * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.75999999999999999e84

   1. Initial program 98.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 1.75999999999999999e84 < 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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   13. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 36.2% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.35 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{b \cdot a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.35e+84) (/ (/ x y) a) (/ (/ x (* b a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.35e+84) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (b * a)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.35d+84) then
        tmp = (x / y) / a
    else
        tmp = (x / (b * a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.35e+84) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (b * a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.35e+84:
		tmp = (x / y) / a
	else:
		tmp = (x / (b * a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.35e+84)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(x / Float64(b * a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.35e+84)
		tmp = (x / y) / a;
	else
		tmp = (x / (b * a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.35e+84], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(b * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.35e84

   1. Initial program 98.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 1.35e84 < 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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 34.0% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 7.2e+84) (/ (/ x y) a) (/ (/ x (* a y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.2e+84) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (a * y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 7.2d+84) then
        tmp = (x / y) / a
    else
        tmp = (x / (a * y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.2e+84) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (a * y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 7.2e+84:
		tmp = (x / y) / a
	else:
		tmp = (x / (a * y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 7.2e+84)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(x / Float64(a * y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 7.2e+84)
		tmp = (x / y) / a;
	else
		tmp = (x / (a * y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 7.2e+84], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 7.1999999999999999e84

   1. Initial program 98.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 7.1999999999999999e84 < 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 t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 31.4% 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 98.9%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in y around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]

8. Taylor expanded in b around 0 0

   \[\leadsto expr\]

10. Simplified 0

    \[\leadsto expr\]

11. Taylor expanded in t around 0 0

    \[\leadsto expr\]

13. Simplified 0

    \[\leadsto expr\]
14. Add Preprocessing

Alternative 25: 30.6% accurate, 63.0× speedup

Math

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

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(x / Float64(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[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.9%

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

3. Taylor expanded in t around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in y around 0 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]

9. Taylor expanded in b around 0 0

   \[\leadsto expr\]

11. Simplified 0

    \[\leadsto expr\]
12. Add Preprocessing

Developer Target 1: 71.5% 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 2024111 
(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))