Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B

Percentage Accurate: 96.5% → 99.6%

Time: 24.0s

Alternatives: 19

Speedup: 1.0×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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)) + (a * (log((1.0d0 - z)) - b))))
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)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) + (a * (log((1.0d0 - z)) - b))))
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)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x \cdot e^{\mathsf{fma}\left(a, \mathsf{log1p}\left(-z\right) - b, y \cdot \left(\log z - t\right)\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (fma a (- (log1p (- z)) b) (* y (- (log z) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(fma(a, (log1p(-z) - b), (y * (log(z) - t))));
}

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(fma(a, Float64(log1p(Float64(-z)) - b), Float64(y * Float64(log(z) - t)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(a * N[(N[Log[1 + (-z)], $MachinePrecision] - b), $MachinePrecision] + N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.9%

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

   1. +-commutative 96.9%

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

   2. fma-def 97.3%

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

   3. sub-neg 97.3%

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

   4. log1p-def 99.9%

      \[\leadsto x \cdot e^{\mathsf{fma}\left(a, \color{blue}{\mathsf{log1p}\left(-z\right)} - b, y \cdot \left(\log z - t\right)\right)} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x \cdot e^{\mathsf{fma}\left(a, \mathsf{log1p}\left(-z\right) - b, y \cdot \left(\log z - t\right)\right)}} \]

4. Final simplification 99.9%

   \[\leadsto x \cdot e^{\mathsf{fma}\left(a, \mathsf{log1p}\left(-z\right) - b, y \cdot \left(\log z - t\right)\right)} \]

Alternative 2: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) + (a * (log((1.0d0 - z)) - b))))
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)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

2. Final simplification 96.9%

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

Alternative 3: 90.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{a \cdot \left(-b\right) - y \cdot t}\\ t_2 := x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-225}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (- (* a (- b)) (* y t)))))
        (t_2 (* x (exp (* y (- (log z) t))))))
   (if (<= y -3.2e+144)
     t_2
     (if (<= y -4e-183)
       t_1
       (if (<= y 5e-225)
         (* x (exp (* a (- (- z) b))))
         (if (<= y 4e+52) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp(((a * -b) - (y * t)));
	double t_2 = x * exp((y * (log(z) - t)));
	double tmp;
	if (y <= -3.2e+144) {
		tmp = t_2;
	} else if (y <= -4e-183) {
		tmp = t_1;
	} else if (y <= 5e-225) {
		tmp = x * exp((a * (-z - b)));
	} else if (y <= 4e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * exp(((a * -b) - (y * t)))
    t_2 = x * exp((y * (log(z) - t)))
    if (y <= (-3.2d+144)) then
        tmp = t_2
    else if (y <= (-4d-183)) then
        tmp = t_1
    else if (y <= 5d-225) then
        tmp = x * exp((a * (-z - b)))
    else if (y <= 4d+52) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp(((a * -b) - (y * t)));
	double t_2 = x * Math.exp((y * (Math.log(z) - t)));
	double tmp;
	if (y <= -3.2e+144) {
		tmp = t_2;
	} else if (y <= -4e-183) {
		tmp = t_1;
	} else if (y <= 5e-225) {
		tmp = x * Math.exp((a * (-z - b)));
	} else if (y <= 4e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp(((a * -b) - (y * t)))
	t_2 = x * math.exp((y * (math.log(z) - t)))
	tmp = 0
	if y <= -3.2e+144:
		tmp = t_2
	elif y <= -4e-183:
		tmp = t_1
	elif y <= 5e-225:
		tmp = x * math.exp((a * (-z - b)))
	elif y <= 4e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(Float64(a * Float64(-b)) - Float64(y * t))))
	t_2 = Float64(x * exp(Float64(y * Float64(log(z) - t))))
	tmp = 0.0
	if (y <= -3.2e+144)
		tmp = t_2;
	elseif (y <= -4e-183)
		tmp = t_1;
	elseif (y <= 5e-225)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	elseif (y <= 4e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp(((a * -b) - (y * t)));
	t_2 = x * exp((y * (log(z) - t)));
	tmp = 0.0;
	if (y <= -3.2e+144)
		tmp = t_2;
	elseif (y <= -4e-183)
		tmp = t_1;
	elseif (y <= 5e-225)
		tmp = x * exp((a * (-z - b)));
	elseif (y <= 4e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(N[(a * (-b)), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+144], t$95$2, If[LessEqual[y, -4e-183], t$95$1, If[LessEqual[y, 5e-225], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2000000000000001e144 or 4e52 < y

   1. Initial program 98.9%

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

   2. Taylor expanded in y around inf 95.7%

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

   if -3.2000000000000001e144 < y < -4.00000000000000002e-183 or 5.0000000000000001e-225 < y < 4e52

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 98.2%

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

   3. Taylor expanded in t around inf 90.9%

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

      1. neg-mul-1 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in a around 0 90.9%

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

      1. neg-mul-1 90.9%

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

      2. mul-1-neg 90.9%

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

      3. unsub-neg 90.9%

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

      4. *-commutative 90.9%

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

      5. distribute-rgt-neg-in 90.9%

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

      6. *-commutative 90.9%

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

   8. Simplified 90.9%

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

   if -4.00000000000000002e-183 < y < 5.0000000000000001e-225

   1. Initial program 88.1%

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

   2. Taylor expanded in y around 0 86.4%

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

      1. sub-neg 86.4%

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

      2. sub-neg 86.4%

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

      3. sub-neg 86.4%

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

      4. neg-mul-1 86.4%

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

      5. log1p-def 98.1%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      6. neg-mul-1 98.1%

         \[\leadsto x \cdot e^{a \cdot \left(\mathsf{log1p}\left(\color{blue}{-z}\right) - b\right)} \]

   4. Simplified 98.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   5. Taylor expanded in z around 0 98.1%

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

      1. associate-*r* 98.1%

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

      2. associate-*r* 98.1%

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

      3. distribute-lft-out 98.1%

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

      4. neg-mul-1 98.1%

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

   7. Simplified 98.1%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+144}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-183}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right) - y \cdot t}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-225}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+52}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right) - y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \]

Alternative 4: 96.0% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

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)) - (a * b)))
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)) - (a * b)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in z around 0 96.1%

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

3. Final simplification 96.1%

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

Alternative 5: 83.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-153} \lor \neg \left(t \leq 4.7 \cdot 10^{-219}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right) - y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.2e-153) (not (<= t 4.7e-219)))
   (* x (exp (- (* a (- b)) (* y t))))
   (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.2e-153) || !(t <= 4.7e-219)) {
		tmp = x * exp(((a * -b) - (y * t)));
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.2d-153)) .or. (.not. (t <= 4.7d-219))) then
        tmp = x * exp(((a * -b) - (y * t)))
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.2e-153) || !(t <= 4.7e-219)) {
		tmp = x * Math.exp(((a * -b) - (y * t)));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.2e-153) or not (t <= 4.7e-219):
		tmp = x * math.exp(((a * -b) - (y * t)))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.2e-153) || !(t <= 4.7e-219))
		tmp = Float64(x * exp(Float64(Float64(a * Float64(-b)) - Float64(y * t))));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.2e-153) || ~((t <= 4.7e-219)))
		tmp = x * exp(((a * -b) - (y * t)));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.2e-153], N[Not[LessEqual[t, 4.7e-219]], $MachinePrecision]], N[(x * N[Exp[N[(N[(a * (-b)), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.20000000000000008e-153 or 4.7e-219 < t

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0 96.3%

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

   3. Taylor expanded in t around inf 88.4%

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

      1. neg-mul-1 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in a around 0 88.4%

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

      1. neg-mul-1 88.4%

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

      2. mul-1-neg 88.4%

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

      3. unsub-neg 88.4%

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

      4. *-commutative 88.4%

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

      5. distribute-rgt-neg-in 88.4%

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

      6. *-commutative 88.4%

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

   8. Simplified 88.4%

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

   if -4.20000000000000008e-153 < t < 4.7e-219

   1. Initial program 97.8%

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

   2. Taylor expanded in y around inf 76.7%

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

   3. Taylor expanded in t around 0 76.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-153} \lor \neg \left(t \leq 4.7 \cdot 10^{-219}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right) - y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 6: 75.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-14} \lor \neg \left(y \leq 3.6 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.5e-14) (not (<= y 3.6e-12)))
   (* x (pow z y))
   (* x (exp (* a (- (- z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.5e-14) || !(y <= 3.6e-12)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp((a * (-z - 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 ((y <= (-1.5d-14)) .or. (.not. (y <= 3.6d-12))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp((a * (-z - 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 ((y <= -1.5e-14) || !(y <= 3.6e-12)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((a * (-z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.5e-14) or not (y <= 3.6e-12):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((a * (-z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.5e-14) || !(y <= 3.6e-12))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.5e-14) || ~((y <= 3.6e-12)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((a * (-z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.5e-14], N[Not[LessEqual[y, 3.6e-12]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4999999999999999e-14 or 3.6e-12 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 89.3%

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

   3. Taylor expanded in t around 0 71.8%

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

   if -1.4999999999999999e-14 < y < 3.6e-12

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0 81.3%

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

      1. sub-neg 81.3%

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

      2. sub-neg 81.3%

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

      3. sub-neg 81.3%

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

      4. neg-mul-1 81.3%

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

      5. log1p-def 86.6%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      6. neg-mul-1 86.6%

         \[\leadsto x \cdot e^{a \cdot \left(\mathsf{log1p}\left(\color{blue}{-z}\right) - b\right)} \]

   4. Simplified 86.6%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   5. Taylor expanded in z around 0 86.6%

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

      1. associate-*r* 86.6%

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

      2. associate-*r* 86.6%

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

      3. distribute-lft-out 86.6%

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

      4. neg-mul-1 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-14} \lor \neg \left(y \leq 3.6 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \]

Alternative 7: 71.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -340 \lor \neg \left(t \leq 2.2 \cdot 10^{+116}\right):\\ \;\;\;\;x \cdot e^{-y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -340.0) (not (<= t 2.2e+116)))
   (* x (exp (- (* y t))))
   (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -340.0) || !(t <= 2.2e+116)) {
		tmp = x * exp(-(y * t));
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-340.0d0)) .or. (.not. (t <= 2.2d+116))) then
        tmp = x * exp(-(y * t))
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -340.0) || !(t <= 2.2e+116)) {
		tmp = x * Math.exp(-(y * t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -340.0) or not (t <= 2.2e+116):
		tmp = x * math.exp(-(y * t))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -340.0) || !(t <= 2.2e+116))
		tmp = Float64(x * exp(Float64(-Float64(y * t))));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -340.0) || ~((t <= 2.2e+116)))
		tmp = x * exp(-(y * t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -340.0], N[Not[LessEqual[t, 2.2e+116]], $MachinePrecision]], N[(x * N[Exp[(-N[(y * t), $MachinePrecision])], $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -340 or 2.2e116 < t

   1. Initial program 95.9%

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

   2. Taylor expanded in t around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. distribute-lft-neg-out 71.4%

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

      3. *-commutative 71.4%

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

   4. Simplified 71.4%

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

   if -340 < t < 2.2e116

   1. Initial program 97.5%

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

   2. Taylor expanded in y around inf 68.0%

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

   3. Taylor expanded in t around 0 68.1%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -340 \lor \neg \left(t \leq 2.2 \cdot 10^{+116}\right):\\ \;\;\;\;x \cdot e^{-y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 8: 73.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-10} \lor \neg \left(y \leq 3.6 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.7e-10) (not (<= y 3.6e-12)))
   (* x (pow z y))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.7e-10) || !(y <= 3.6e-12)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp((a * -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 ((y <= (-1.7d-10)) .or. (.not. (y <= 3.6d-12))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp((a * -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 ((y <= -1.7e-10) || !(y <= 3.6e-12)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.7e-10) or not (y <= 3.6e-12):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.7e-10) || !(y <= 3.6e-12))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.7e-10) || ~((y <= 3.6e-12)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.7e-10], N[Not[LessEqual[y, 3.6e-12]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.70000000000000007e-10 or 3.6e-12 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 89.2%

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

   3. Taylor expanded in t around 0 72.4%

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

   if -1.70000000000000007e-10 < y < 3.6e-12

   1. Initial program 94.6%

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

   2. Taylor expanded in b around inf 79.9%

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

      1. associate-*r* 79.9%

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

      2. neg-mul-1 79.9%

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

   4. Simplified 79.9%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-10} \lor \neg \left(y \leq 3.6 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 9: 56.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right) \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.7e-8) (* t (* (* t (* y (* x y))) 0.5)) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.7e-8) {
		tmp = t * ((t * (y * (x * y))) * 0.5);
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5.7d-8)) then
        tmp = t * ((t * (y * (x * y))) * 0.5d0)
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.7e-8) {
		tmp = t * ((t * (y * (x * y))) * 0.5);
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.7e-8:
		tmp = t * ((t * (y * (x * y))) * 0.5)
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.7e-8)
		tmp = Float64(t * Float64(Float64(t * Float64(y * Float64(x * y))) * 0.5));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.7e-8)
		tmp = t * ((t * (y * (x * y))) * 0.5);
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.7e-8], N[(t * N[(N[(t * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.70000000000000009e-8

   1. Initial program 95.4%

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

   2. Taylor expanded in t around inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. distribute-lft-neg-out 65.9%

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

      3. *-commutative 65.9%

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

   4. Simplified 65.9%

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

   5. Taylor expanded in y around 0 33.2%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(t \cdot \left(x \cdot y\right)\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 33.2%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]

      2. mul-1-neg 33.2%

         \[\leadsto \left(x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)}\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      3. unsub-neg 33.2%

         \[\leadsto \color{blue}{\left(x - t \cdot \left(x \cdot y\right)\right)} + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      4. associate-*r* 33.2%

         \[\leadsto \left(x - \color{blue}{\left(t \cdot x\right) \cdot y}\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      5. unpow2 33.2%

         \[\leadsto \left(x - \left(t \cdot x\right) \cdot y\right) + 0.5 \cdot \left(\color{blue}{\left(t \cdot t\right)} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      6. *-commutative 33.2%

         \[\leadsto \left(x - \left(t \cdot x\right) \cdot y\right) + 0.5 \cdot \left(\left(t \cdot t\right) \cdot \color{blue}{\left({y}^{2} \cdot x\right)}\right) \]

      7. unpow2 33.2%

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

   7. Simplified 33.2%

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

   8. Taylor expanded in t around inf 38.5%

      \[\leadsto \color{blue}{0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 38.5%

         \[\leadsto \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot 0.5} \]

      2. unpow2 38.5%

         \[\leadsto \left(\color{blue}{\left(t \cdot t\right)} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot 0.5 \]

      3. *-commutative 38.5%

         \[\leadsto \left(\left(t \cdot t\right) \cdot \color{blue}{\left({y}^{2} \cdot x\right)}\right) \cdot 0.5 \]

      4. unpow2 38.5%

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

      5. associate-*r* 37.1%

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

      6. associate-*r* 40.7%

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

      7. associate-*l* 40.7%

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

   10. Simplified 40.7%

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

   if -5.70000000000000009e-8 < t

   1. Initial program 97.4%

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

   2. Taylor expanded in y around inf 70.5%

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

   3. Taylor expanded in t around 0 66.5%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right) \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 10: 38.7% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \left(\left(y \cdot y\right) \cdot \left(t \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(\left(1 - y \cdot t\right) + 0.5 \cdot \left(\left(y \cdot t\right) \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right) \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.42e-39)
   (* x (* 0.5 (* (* y y) (* t t))))
   (if (<= b 6.5e+54)
     (* x (+ (- 1.0 (* y t)) (* 0.5 (* (* y t) (* y t)))))
     (* t (* (* t (* y (* x y))) 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.42e-39) {
		tmp = x * (0.5 * ((y * y) * (t * t)));
	} else if (b <= 6.5e+54) {
		tmp = x * ((1.0 - (y * t)) + (0.5 * ((y * t) * (y * t))));
	} else {
		tmp = t * ((t * (y * (x * y))) * 0.5);
	}
	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 <= (-1.42d-39)) then
        tmp = x * (0.5d0 * ((y * y) * (t * t)))
    else if (b <= 6.5d+54) then
        tmp = x * ((1.0d0 - (y * t)) + (0.5d0 * ((y * t) * (y * t))))
    else
        tmp = t * ((t * (y * (x * y))) * 0.5d0)
    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 <= -1.42e-39) {
		tmp = x * (0.5 * ((y * y) * (t * t)));
	} else if (b <= 6.5e+54) {
		tmp = x * ((1.0 - (y * t)) + (0.5 * ((y * t) * (y * t))));
	} else {
		tmp = t * ((t * (y * (x * y))) * 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.42e-39:
		tmp = x * (0.5 * ((y * y) * (t * t)))
	elif b <= 6.5e+54:
		tmp = x * ((1.0 - (y * t)) + (0.5 * ((y * t) * (y * t))))
	else:
		tmp = t * ((t * (y * (x * y))) * 0.5)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.42e-39)
		tmp = Float64(x * Float64(0.5 * Float64(Float64(y * y) * Float64(t * t))));
	elseif (b <= 6.5e+54)
		tmp = Float64(x * Float64(Float64(1.0 - Float64(y * t)) + Float64(0.5 * Float64(Float64(y * t) * Float64(y * t)))));
	else
		tmp = Float64(t * Float64(Float64(t * Float64(y * Float64(x * y))) * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.42e-39)
		tmp = x * (0.5 * ((y * y) * (t * t)));
	elseif (b <= 6.5e+54)
		tmp = x * ((1.0 - (y * t)) + (0.5 * ((y * t) * (y * t))));
	else
		tmp = t * ((t * (y * (x * y))) * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.42e-39], N[(x * N[(0.5 * N[(N[(y * y), $MachinePrecision] * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+54], N[(x * N[(N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(y * t), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(t * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.42000000000000005e-39

   1. Initial program 98.6%

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

   2. Taylor expanded in t around inf 41.5%

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

      1. mul-1-neg 41.5%

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

      2. distribute-lft-neg-out 41.5%

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

      3. *-commutative 41.5%

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

   4. Simplified 41.5%

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

   5. Taylor expanded in y around 0 26.6%

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-1 \cdot \left(t \cdot y\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 26.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -1 \cdot \left(t \cdot y\right)\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)} \]

      2. mul-1-neg 26.6%

         \[\leadsto x \cdot \left(\left(1 + \color{blue}{\left(-t \cdot y\right)}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      3. unsub-neg 26.6%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - t \cdot y\right)} + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      4. *-commutative 26.6%

         \[\leadsto x \cdot \left(\left(1 - \color{blue}{y \cdot t}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      5. *-commutative 26.6%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + 0.5 \cdot \color{blue}{\left({y}^{2} \cdot {t}^{2}\right)}\right) \]

      6. unpow2 26.6%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + 0.5 \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot {t}^{2}\right)\right) \]

      7. unpow2 26.6%

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

      8. unswap-sqr 25.7%

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

   7. Simplified 25.7%

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

   8. Taylor expanded in y around inf 45.5%

      \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 45.5%

         \[\leadsto x \cdot \left(0.5 \cdot \color{blue}{\left({y}^{2} \cdot {t}^{2}\right)}\right) \]

      2. unpow2 45.5%

         \[\leadsto x \cdot \left(0.5 \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot {t}^{2}\right)\right) \]

      3. unpow2 45.5%

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

   10. Simplified 45.5%

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

   if -1.42000000000000005e-39 < b < 6.5e54

   1. Initial program 94.9%

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

   2. Taylor expanded in t around inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. distribute-lft-neg-out 64.7%

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

      3. *-commutative 64.7%

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

   4. Simplified 64.7%

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

   5. Taylor expanded in y around 0 42.6%

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-1 \cdot \left(t \cdot y\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 42.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -1 \cdot \left(t \cdot y\right)\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)} \]

      2. mul-1-neg 42.6%

         \[\leadsto x \cdot \left(\left(1 + \color{blue}{\left(-t \cdot y\right)}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      3. unsub-neg 42.6%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - t \cdot y\right)} + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      4. *-commutative 42.6%

         \[\leadsto x \cdot \left(\left(1 - \color{blue}{y \cdot t}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      5. *-commutative 42.6%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + 0.5 \cdot \color{blue}{\left({y}^{2} \cdot {t}^{2}\right)}\right) \]

      6. unpow2 42.6%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + 0.5 \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot {t}^{2}\right)\right) \]

      7. unpow2 42.6%

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

      8. unswap-sqr 43.2%

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

   7. Simplified 43.2%

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

   if 6.5e54 < b

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 36.7%

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

      1. mul-1-neg 36.7%

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

      2. distribute-lft-neg-out 36.7%

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

      3. *-commutative 36.7%

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

   4. Simplified 36.7%

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

   5. Taylor expanded in y around 0 23.4%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(t \cdot \left(x \cdot y\right)\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 23.4%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]

      2. mul-1-neg 23.4%

         \[\leadsto \left(x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)}\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      3. unsub-neg 23.4%

         \[\leadsto \color{blue}{\left(x - t \cdot \left(x \cdot y\right)\right)} + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      4. associate-*r* 23.4%

         \[\leadsto \left(x - \color{blue}{\left(t \cdot x\right) \cdot y}\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      5. unpow2 23.4%

         \[\leadsto \left(x - \left(t \cdot x\right) \cdot y\right) + 0.5 \cdot \left(\color{blue}{\left(t \cdot t\right)} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      6. *-commutative 23.4%

         \[\leadsto \left(x - \left(t \cdot x\right) \cdot y\right) + 0.5 \cdot \left(\left(t \cdot t\right) \cdot \color{blue}{\left({y}^{2} \cdot x\right)}\right) \]

      7. unpow2 23.4%

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

   7. Simplified 23.4%

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

   8. Taylor expanded in t around inf 35.4%

      \[\leadsto \color{blue}{0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot 0.5} \]

      2. unpow2 35.4%

         \[\leadsto \left(\color{blue}{\left(t \cdot t\right)} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot 0.5 \]

      3. *-commutative 35.4%

         \[\leadsto \left(\left(t \cdot t\right) \cdot \color{blue}{\left({y}^{2} \cdot x\right)}\right) \cdot 0.5 \]

      4. unpow2 35.4%

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

      5. associate-*r* 37.6%

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

      6. associate-*r* 44.0%

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

      7. associate-*l* 44.0%

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

   10. Simplified 44.0%

       \[\leadsto \color{blue}{t \cdot \left(\left(t \cdot \left(y \cdot \left(y \cdot x\right)\right)\right) \cdot 0.5\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \left(\left(y \cdot y\right) \cdot \left(t \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(\left(1 - y \cdot t\right) + 0.5 \cdot \left(\left(y \cdot t\right) \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right) \cdot 0.5\right)\\ \end{array} \]

Alternative 11: 37.9% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right) \cdot 0.5\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-279}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \left(1 - a \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \left(\left(y \cdot y\right) \cdot \left(t \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* (* t (* y (* x y))) 0.5))))
   (if (<= y -6.4e-41)
     t_1
     (if (<= y -2.2e-279)
       (- x (* t (* x y)))
       (if (<= y 3.2e-242)
         t_1
         (if (<= y 9.5e-79)
           (* x (- 1.0 (* a z)))
           (* x (* 0.5 (* (* y y) (* t t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * ((t * (y * (x * y))) * 0.5);
	double tmp;
	if (y <= -6.4e-41) {
		tmp = t_1;
	} else if (y <= -2.2e-279) {
		tmp = x - (t * (x * y));
	} else if (y <= 3.2e-242) {
		tmp = t_1;
	} else if (y <= 9.5e-79) {
		tmp = x * (1.0 - (a * z));
	} else {
		tmp = x * (0.5 * ((y * y) * (t * t)));
	}
	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 = t * ((t * (y * (x * y))) * 0.5d0)
    if (y <= (-6.4d-41)) then
        tmp = t_1
    else if (y <= (-2.2d-279)) then
        tmp = x - (t * (x * y))
    else if (y <= 3.2d-242) then
        tmp = t_1
    else if (y <= 9.5d-79) then
        tmp = x * (1.0d0 - (a * z))
    else
        tmp = x * (0.5d0 * ((y * y) * (t * t)))
    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 = t * ((t * (y * (x * y))) * 0.5);
	double tmp;
	if (y <= -6.4e-41) {
		tmp = t_1;
	} else if (y <= -2.2e-279) {
		tmp = x - (t * (x * y));
	} else if (y <= 3.2e-242) {
		tmp = t_1;
	} else if (y <= 9.5e-79) {
		tmp = x * (1.0 - (a * z));
	} else {
		tmp = x * (0.5 * ((y * y) * (t * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * ((t * (y * (x * y))) * 0.5)
	tmp = 0
	if y <= -6.4e-41:
		tmp = t_1
	elif y <= -2.2e-279:
		tmp = x - (t * (x * y))
	elif y <= 3.2e-242:
		tmp = t_1
	elif y <= 9.5e-79:
		tmp = x * (1.0 - (a * z))
	else:
		tmp = x * (0.5 * ((y * y) * (t * t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(Float64(t * Float64(y * Float64(x * y))) * 0.5))
	tmp = 0.0
	if (y <= -6.4e-41)
		tmp = t_1;
	elseif (y <= -2.2e-279)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (y <= 3.2e-242)
		tmp = t_1;
	elseif (y <= 9.5e-79)
		tmp = Float64(x * Float64(1.0 - Float64(a * z)));
	else
		tmp = Float64(x * Float64(0.5 * Float64(Float64(y * y) * Float64(t * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * ((t * (y * (x * y))) * 0.5);
	tmp = 0.0;
	if (y <= -6.4e-41)
		tmp = t_1;
	elseif (y <= -2.2e-279)
		tmp = x - (t * (x * y));
	elseif (y <= 3.2e-242)
		tmp = t_1;
	elseif (y <= 9.5e-79)
		tmp = x * (1.0 - (a * z));
	else
		tmp = x * (0.5 * ((y * y) * (t * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(N[(t * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e-41], t$95$1, If[LessEqual[y, -2.2e-279], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-242], t$95$1, If[LessEqual[y, 9.5e-79], N[(x * N[(1.0 - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.5 * N[(N[(y * y), $MachinePrecision] * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.40000000000000024e-41 or -2.2e-279 < y < 3.19999999999999999e-242

   1. Initial program 96.6%

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

   2. Taylor expanded in t around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. distribute-lft-neg-out 46.2%

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

      3. *-commutative 46.2%

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

   4. Simplified 46.2%

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

   5. Taylor expanded in y around 0 28.1%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(t \cdot \left(x \cdot y\right)\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 28.1%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]

      2. mul-1-neg 28.1%

         \[\leadsto \left(x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)}\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      3. unsub-neg 28.1%

         \[\leadsto \color{blue}{\left(x - t \cdot \left(x \cdot y\right)\right)} + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      4. associate-*r* 30.3%

         \[\leadsto \left(x - \color{blue}{\left(t \cdot x\right) \cdot y}\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      5. unpow2 30.3%

         \[\leadsto \left(x - \left(t \cdot x\right) \cdot y\right) + 0.5 \cdot \left(\color{blue}{\left(t \cdot t\right)} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      6. *-commutative 30.3%

         \[\leadsto \left(x - \left(t \cdot x\right) \cdot y\right) + 0.5 \cdot \left(\left(t \cdot t\right) \cdot \color{blue}{\left({y}^{2} \cdot x\right)}\right) \]

      7. unpow2 30.3%

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

   7. Simplified 30.3%

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

   8. Taylor expanded in t around inf 42.3%

      \[\leadsto \color{blue}{0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 42.3%

         \[\leadsto \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot 0.5} \]

      2. unpow2 42.3%

         \[\leadsto \left(\color{blue}{\left(t \cdot t\right)} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot 0.5 \]

      3. *-commutative 42.3%

         \[\leadsto \left(\left(t \cdot t\right) \cdot \color{blue}{\left({y}^{2} \cdot x\right)}\right) \cdot 0.5 \]

      4. unpow2 42.3%

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

      5. associate-*r* 42.4%

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

      6. associate-*r* 52.5%

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

      7. associate-*l* 52.5%

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

   10. Simplified 52.5%

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

   if -6.40000000000000024e-41 < y < -2.2e-279

   1. Initial program 93.9%

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

   2. Taylor expanded in t around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. distribute-lft-neg-out 58.9%

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

      3. *-commutative 58.9%

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

   4. Simplified 58.9%

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

   5. Taylor expanded in y around 0 43.3%

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

      1. associate-*r* 43.3%

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

      2. neg-mul-1 43.3%

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

      3. *-commutative 43.3%

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

   7. Simplified 43.3%

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

   if 3.19999999999999999e-242 < y < 9.4999999999999997e-79

   1. Initial program 94.8%

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

   2. Taylor expanded in y around 0 79.7%

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

      1. sub-neg 79.7%

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

      2. sub-neg 79.7%

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

      3. sub-neg 79.7%

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

      4. neg-mul-1 79.7%

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

      5. log1p-def 87.6%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      6. neg-mul-1 87.6%

         \[\leadsto x \cdot e^{a \cdot \left(\mathsf{log1p}\left(\color{blue}{-z}\right) - b\right)} \]

   4. Simplified 87.6%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   5. Taylor expanded in b around 0 34.2%

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

   6. Taylor expanded in z around 0 39.3%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 39.3%

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

      2. unsub-neg 39.3%

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

   8. Simplified 39.3%

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

   if 9.4999999999999997e-79 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 56.3%

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

      1. mul-1-neg 56.3%

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

      2. distribute-lft-neg-out 56.3%

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

      3. *-commutative 56.3%

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

   4. Simplified 56.3%

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

   5. Taylor expanded in y around 0 28.1%

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-1 \cdot \left(t \cdot y\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 28.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -1 \cdot \left(t \cdot y\right)\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)} \]

      2. mul-1-neg 28.1%

         \[\leadsto x \cdot \left(\left(1 + \color{blue}{\left(-t \cdot y\right)}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      3. unsub-neg 28.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - t \cdot y\right)} + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      4. *-commutative 28.1%

         \[\leadsto x \cdot \left(\left(1 - \color{blue}{y \cdot t}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      5. *-commutative 28.1%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + 0.5 \cdot \color{blue}{\left({y}^{2} \cdot {t}^{2}\right)}\right) \]

      6. unpow2 28.1%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + 0.5 \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot {t}^{2}\right)\right) \]

      7. unpow2 28.1%

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

      8. unswap-sqr 27.3%

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

   7. Simplified 27.3%

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

   8. Taylor expanded in y around inf 34.7%

      \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 34.7%

         \[\leadsto x \cdot \left(0.5 \cdot \color{blue}{\left({y}^{2} \cdot {t}^{2}\right)}\right) \]

      2. unpow2 34.7%

         \[\leadsto x \cdot \left(0.5 \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot {t}^{2}\right)\right) \]

      3. unpow2 34.7%

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

   10. Simplified 34.7%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right) \cdot 0.5\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-279}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right) \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \left(1 - a \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \left(\left(y \cdot y\right) \cdot \left(t \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 12: 33.5% accurate, 20.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-42} \lor \neg \left(b \leq 3.8 \cdot 10^{+65}\right):\\ \;\;\;\;0.5 \cdot \left(\left(t \cdot t\right) \cdot \left(x \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.4e-42) (not (<= b 3.8e+65)))
   (* 0.5 (* (* t t) (* x (* y y))))
   (- x (* t (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.4e-42) || !(b <= 3.8e+65)) {
		tmp = 0.5 * ((t * t) * (x * (y * y)));
	} else {
		tmp = x - (t * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4.4d-42)) .or. (.not. (b <= 3.8d+65))) then
        tmp = 0.5d0 * ((t * t) * (x * (y * y)))
    else
        tmp = x - (t * (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.4e-42) || !(b <= 3.8e+65)) {
		tmp = 0.5 * ((t * t) * (x * (y * y)));
	} else {
		tmp = x - (t * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.4e-42) or not (b <= 3.8e+65):
		tmp = 0.5 * ((t * t) * (x * (y * y)))
	else:
		tmp = x - (t * (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.4e-42) || !(b <= 3.8e+65))
		tmp = Float64(0.5 * Float64(Float64(t * t) * Float64(x * Float64(y * y))));
	else
		tmp = Float64(x - Float64(t * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.4e-42) || ~((b <= 3.8e+65)))
		tmp = 0.5 * ((t * t) * (x * (y * y)));
	else
		tmp = x - (t * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.4e-42], N[Not[LessEqual[b, 3.8e+65]], $MachinePrecision]], N[(0.5 * N[(N[(t * t), $MachinePrecision] * N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.4000000000000001e-42 or 3.80000000000000011e65 < b

   1. Initial program 99.2%

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

   2. Taylor expanded in t around inf 39.1%

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

      1. mul-1-neg 39.1%

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

      2. distribute-lft-neg-out 39.1%

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

      3. *-commutative 39.1%

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

   4. Simplified 39.1%

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

   5. Taylor expanded in y around 0 23.3%

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-1 \cdot \left(t \cdot y\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 23.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -1 \cdot \left(t \cdot y\right)\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)} \]

      2. mul-1-neg 23.3%

         \[\leadsto x \cdot \left(\left(1 + \color{blue}{\left(-t \cdot y\right)}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      3. unsub-neg 23.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - t \cdot y\right)} + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      4. *-commutative 23.3%

         \[\leadsto x \cdot \left(\left(1 - \color{blue}{y \cdot t}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      5. *-commutative 23.3%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + 0.5 \cdot \color{blue}{\left({y}^{2} \cdot {t}^{2}\right)}\right) \]

      6. unpow2 23.3%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + 0.5 \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot {t}^{2}\right)\right) \]

      7. unpow2 23.3%

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

      8. unswap-sqr 22.1%

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

   7. Simplified 22.1%

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

   8. Taylor expanded in y around inf 41.1%

      \[\leadsto \color{blue}{0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. unpow2 41.1%

         \[\leadsto 0.5 \cdot \left(\color{blue}{\left(t \cdot t\right)} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      2. unpow2 41.1%

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

   10. Simplified 41.1%

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

   if -4.4000000000000001e-42 < b < 3.80000000000000011e65

   1. Initial program 94.9%

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

   2. Taylor expanded in t around inf 65.0%

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

      1. mul-1-neg 65.0%

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

      2. distribute-lft-neg-out 65.0%

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

      3. *-commutative 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in y around 0 38.1%

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

      1. associate-*r* 38.1%

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

      2. neg-mul-1 38.1%

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

      3. *-commutative 38.1%

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

   7. Simplified 38.1%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-42} \lor \neg \left(b \leq 3.8 \cdot 10^{+65}\right):\\ \;\;\;\;0.5 \cdot \left(\left(t \cdot t\right) \cdot \left(x \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 13: 35.2% accurate, 20.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{-42} \lor \neg \left(b \leq 2 \cdot 10^{+73}\right):\\ \;\;\;\;t \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right) \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.05e-42) (not (<= b 2e+73)))
   (* t (* (* t (* y (* x y))) 0.5))
   (- x (* t (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.05e-42) || !(b <= 2e+73)) {
		tmp = t * ((t * (y * (x * y))) * 0.5);
	} else {
		tmp = x - (t * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.05d-42)) .or. (.not. (b <= 2d+73))) then
        tmp = t * ((t * (y * (x * y))) * 0.5d0)
    else
        tmp = x - (t * (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.05e-42) || !(b <= 2e+73)) {
		tmp = t * ((t * (y * (x * y))) * 0.5);
	} else {
		tmp = x - (t * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.05e-42) or not (b <= 2e+73):
		tmp = t * ((t * (y * (x * y))) * 0.5)
	else:
		tmp = x - (t * (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.05e-42) || !(b <= 2e+73))
		tmp = Float64(t * Float64(Float64(t * Float64(y * Float64(x * y))) * 0.5));
	else
		tmp = Float64(x - Float64(t * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.05e-42) || ~((b <= 2e+73)))
		tmp = t * ((t * (y * (x * y))) * 0.5);
	else
		tmp = x - (t * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.05e-42], N[Not[LessEqual[b, 2e+73]], $MachinePrecision]], N[(t * N[(N[(t * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.0500000000000001e-42 or 1.99999999999999997e73 < b

   1. Initial program 99.2%

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

   2. Taylor expanded in t around inf 39.1%

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

      1. mul-1-neg 39.1%

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

      2. distribute-lft-neg-out 39.1%

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

      3. *-commutative 39.1%

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

   4. Simplified 39.1%

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

   5. Taylor expanded in y around 0 23.8%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(t \cdot \left(x \cdot y\right)\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 23.8%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]

      2. mul-1-neg 23.8%

         \[\leadsto \left(x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)}\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      3. unsub-neg 23.8%

         \[\leadsto \color{blue}{\left(x - t \cdot \left(x \cdot y\right)\right)} + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      4. associate-*r* 23.0%

         \[\leadsto \left(x - \color{blue}{\left(t \cdot x\right) \cdot y}\right) + 0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      5. unpow2 23.0%

         \[\leadsto \left(x - \left(t \cdot x\right) \cdot y\right) + 0.5 \cdot \left(\color{blue}{\left(t \cdot t\right)} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      6. *-commutative 23.0%

         \[\leadsto \left(x - \left(t \cdot x\right) \cdot y\right) + 0.5 \cdot \left(\left(t \cdot t\right) \cdot \color{blue}{\left({y}^{2} \cdot x\right)}\right) \]

      7. unpow2 23.0%

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

   7. Simplified 23.0%

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

   8. Taylor expanded in t around inf 41.1%

      \[\leadsto \color{blue}{0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot 0.5} \]

      2. unpow2 41.1%

         \[\leadsto \left(\color{blue}{\left(t \cdot t\right)} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot 0.5 \]

      3. *-commutative 41.1%

         \[\leadsto \left(\left(t \cdot t\right) \cdot \color{blue}{\left({y}^{2} \cdot x\right)}\right) \cdot 0.5 \]

      4. unpow2 41.1%

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

      5. associate-*r* 42.0%

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

      6. associate-*r* 44.8%

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

      7. associate-*l* 44.8%

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

   10. Simplified 44.8%

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

   if -2.0500000000000001e-42 < b < 1.99999999999999997e73

   1. Initial program 94.9%

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

   2. Taylor expanded in t around inf 65.0%

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

      1. mul-1-neg 65.0%

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

      2. distribute-lft-neg-out 65.0%

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

      3. *-commutative 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in y around 0 38.1%

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

      1. associate-*r* 38.1%

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

      2. neg-mul-1 38.1%

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

      3. *-commutative 38.1%

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

   7. Simplified 38.1%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{-42} \lor \neg \left(b \leq 2 \cdot 10^{+73}\right):\\ \;\;\;\;t \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right) \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 14: 28.3% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(1 - a \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8e-41)
   (* t (* y (- x)))
   (if (<= y 3.1e-69) (* x (- 1.0 (* a z))) (* (* x t) (- y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e-41) {
		tmp = t * (y * -x);
	} else if (y <= 3.1e-69) {
		tmp = x * (1.0 - (a * z));
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8d-41)) then
        tmp = t * (y * -x)
    else if (y <= 3.1d-69) then
        tmp = x * (1.0d0 - (a * z))
    else
        tmp = (x * t) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e-41) {
		tmp = t * (y * -x);
	} else if (y <= 3.1e-69) {
		tmp = x * (1.0 - (a * z));
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8e-41:
		tmp = t * (y * -x)
	elif y <= 3.1e-69:
		tmp = x * (1.0 - (a * z))
	else:
		tmp = (x * t) * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8e-41)
		tmp = Float64(t * Float64(y * Float64(-x)));
	elseif (y <= 3.1e-69)
		tmp = Float64(x * Float64(1.0 - Float64(a * z)));
	else
		tmp = Float64(Float64(x * t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8e-41)
		tmp = t * (y * -x);
	elseif (y <= 3.1e-69)
		tmp = x * (1.0 - (a * z));
	else
		tmp = (x * t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8e-41], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-69], N[(x * N[(1.0 - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000005e-41

   1. Initial program 98.5%

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

   2. Taylor expanded in t around inf 52.7%

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

      1. mul-1-neg 52.7%

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

      2. distribute-lft-neg-out 52.7%

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

      3. *-commutative 52.7%

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

   4. Simplified 52.7%

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

   5. Taylor expanded in y around 0 17.5%

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

      1. mul-1-neg 17.5%

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

      2. unsub-neg 17.5%

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

      3. *-commutative 17.5%

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

   7. Simplified 17.5%

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

   8. Taylor expanded in y around inf 22.4%

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

      1. mul-1-neg 22.4%

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

      2. *-commutative 22.4%

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

      3. distribute-rgt-neg-in 22.4%

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

   10. Simplified 22.4%

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

   if -8.00000000000000005e-41 < y < 3.0999999999999999e-69

   1. Initial program 93.8%

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

   2. Taylor expanded in y around 0 81.4%

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

      1. sub-neg 81.4%

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

      2. sub-neg 81.4%

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

      3. sub-neg 81.4%

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

      4. neg-mul-1 81.4%

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

      5. log1p-def 87.4%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      6. neg-mul-1 87.4%

         \[\leadsto x \cdot e^{a \cdot \left(\mathsf{log1p}\left(\color{blue}{-z}\right) - b\right)} \]

   4. Simplified 87.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   5. Taylor expanded in b around 0 37.1%

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

   6. Taylor expanded in z around 0 38.7%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 38.7%

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

      2. unsub-neg 38.7%

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

   8. Simplified 38.7%

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

   if 3.0999999999999999e-69 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. distribute-lft-neg-out 55.9%

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

      3. *-commutative 55.9%

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

   4. Simplified 55.9%

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

   5. Taylor expanded in y around 0 22.3%

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

      1. mul-1-neg 22.3%

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

      2. unsub-neg 22.3%

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

      3. *-commutative 22.3%

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

   7. Simplified 22.3%

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

   8. Taylor expanded in y around inf 23.2%

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

      1. mul-1-neg 23.2%

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

      2. associate-*r* 26.5%

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

      3. *-commutative 26.5%

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

   10. Simplified 26.5%

       \[\leadsto \color{blue}{-y \cdot \left(t \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(1 - a \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \]

Alternative 15: 28.0% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+53}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{+88}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.6e+53)
   (* (* x t) (- y))
   (if (<= b 1.22e+88) (- x (* t (* x y))) (* t (* y (- x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e+53) {
		tmp = (x * t) * -y;
	} else if (b <= 1.22e+88) {
		tmp = x - (t * (x * y));
	} else {
		tmp = t * (y * -x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.6d+53)) then
        tmp = (x * t) * -y
    else if (b <= 1.22d+88) then
        tmp = x - (t * (x * y))
    else
        tmp = t * (y * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e+53) {
		tmp = (x * t) * -y;
	} else if (b <= 1.22e+88) {
		tmp = x - (t * (x * y));
	} else {
		tmp = t * (y * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.6e+53:
		tmp = (x * t) * -y
	elif b <= 1.22e+88:
		tmp = x - (t * (x * y))
	else:
		tmp = t * (y * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.6e+53)
		tmp = Float64(Float64(x * t) * Float64(-y));
	elseif (b <= 1.22e+88)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	else
		tmp = Float64(t * Float64(y * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.6e+53)
		tmp = (x * t) * -y;
	elseif (b <= 1.22e+88)
		tmp = x - (t * (x * y));
	else
		tmp = t * (y * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.6e+53], N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[b, 1.22e+88], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.6e53

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 30.0%

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

      1. mul-1-neg 30.0%

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

      2. distribute-lft-neg-out 30.0%

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

      3. *-commutative 30.0%

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

   4. Simplified 30.0%

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

   5. Taylor expanded in y around 0 12.7%

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

      1. mul-1-neg 12.7%

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

      2. unsub-neg 12.7%

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

      3. *-commutative 12.7%

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

   7. Simplified 12.7%

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

   8. Taylor expanded in y around inf 29.5%

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

      1. mul-1-neg 29.5%

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

      2. associate-*r* 32.7%

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

      3. *-commutative 32.7%

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

   10. Simplified 32.7%

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

   if -1.6e53 < b < 1.22e88

   1. Initial program 95.7%

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

   2. Taylor expanded in t around inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. distribute-lft-neg-out 64.5%

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

      3. *-commutative 64.5%

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

   4. Simplified 64.5%

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

   5. Taylor expanded in y around 0 36.4%

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

      1. associate-*r* 36.4%

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

      2. neg-mul-1 36.4%

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

      3. *-commutative 36.4%

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

   7. Simplified 36.4%

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

   if 1.22e88 < b

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 36.6%

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

      1. mul-1-neg 36.6%

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

      2. distribute-lft-neg-out 36.6%

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

      3. *-commutative 36.6%

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

   4. Simplified 36.6%

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

   5. Taylor expanded in y around 0 14.8%

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

      1. mul-1-neg 14.8%

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

      2. unsub-neg 14.8%

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

      3. *-commutative 14.8%

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

   7. Simplified 14.8%

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

   8. Taylor expanded in y around inf 23.8%

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

      1. mul-1-neg 23.8%

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

      2. *-commutative 23.8%

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

      3. distribute-rgt-neg-in 23.8%

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

   10. Simplified 23.8%

       \[\leadsto \color{blue}{t \cdot \left(-y \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+53}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{+88}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 16: 27.4% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-41} \lor \neg \left(y \leq 1.65 \cdot 10^{-68}\right):\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e-41) (not (<= y 1.65e-68))) (* (* x t) (- y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e-41) || !(y <= 1.65e-68)) {
		tmp = (x * t) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.7d-41)) .or. (.not. (y <= 1.65d-68))) then
        tmp = (x * t) * -y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e-41) || !(y <= 1.65e-68)) {
		tmp = (x * t) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.7e-41) or not (y <= 1.65e-68):
		tmp = (x * t) * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.7e-41) || !(y <= 1.65e-68))
		tmp = Float64(Float64(x * t) * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.7e-41) || ~((y <= 1.65e-68)))
		tmp = (x * t) * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.7e-41], N[Not[LessEqual[y, 1.65e-68]], $MachinePrecision]], N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e-41 or 1.6499999999999999e-68 < y

   1. Initial program 99.3%

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

   2. Taylor expanded in t around inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. distribute-lft-neg-out 54.5%

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

      3. *-commutative 54.5%

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

   4. Simplified 54.5%

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

   5. Taylor expanded in y around 0 20.1%

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

      1. mul-1-neg 20.1%

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

      2. unsub-neg 20.1%

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

      3. *-commutative 20.1%

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

   7. Simplified 20.1%

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

   8. Taylor expanded in y around inf 22.9%

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

      1. mul-1-neg 22.9%

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

      2. associate-*r* 23.1%

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

      3. *-commutative 23.1%

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

   10. Simplified 23.1%

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

   if -2.7e-41 < y < 1.6499999999999999e-68

   1. Initial program 93.8%

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

   2. Taylor expanded in t around inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. distribute-lft-neg-out 50.8%

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

      3. *-commutative 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in y around 0 35.4%

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

4. Final simplification 28.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-41} \lor \neg \left(y \leq 1.65 \cdot 10^{-68}\right):\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 28.0% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8e-41) (* t (* y (- x))) (if (<= y 4.2e-69) x (* (* x t) (- y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e-41) {
		tmp = t * (y * -x);
	} else if (y <= 4.2e-69) {
		tmp = x;
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8d-41)) then
        tmp = t * (y * -x)
    else if (y <= 4.2d-69) then
        tmp = x
    else
        tmp = (x * t) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e-41) {
		tmp = t * (y * -x);
	} else if (y <= 4.2e-69) {
		tmp = x;
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8e-41:
		tmp = t * (y * -x)
	elif y <= 4.2e-69:
		tmp = x
	else:
		tmp = (x * t) * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8e-41)
		tmp = Float64(t * Float64(y * Float64(-x)));
	elseif (y <= 4.2e-69)
		tmp = x;
	else
		tmp = Float64(Float64(x * t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8e-41)
		tmp = t * (y * -x);
	elseif (y <= 4.2e-69)
		tmp = x;
	else
		tmp = (x * t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8e-41], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-69], x, N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000005e-41

   1. Initial program 98.5%

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

   2. Taylor expanded in t around inf 52.7%

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

      1. mul-1-neg 52.7%

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

      2. distribute-lft-neg-out 52.7%

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

      3. *-commutative 52.7%

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

   4. Simplified 52.7%

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

   5. Taylor expanded in y around 0 17.5%

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

      1. mul-1-neg 17.5%

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

      2. unsub-neg 17.5%

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

      3. *-commutative 17.5%

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

   7. Simplified 17.5%

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

   8. Taylor expanded in y around inf 22.4%

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

      1. mul-1-neg 22.4%

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

      2. *-commutative 22.4%

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

      3. distribute-rgt-neg-in 22.4%

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

   10. Simplified 22.4%

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

   if -8.00000000000000005e-41 < y < 4.1999999999999999e-69

   1. Initial program 93.8%

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

   2. Taylor expanded in t around inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. distribute-lft-neg-out 50.8%

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

      3. *-commutative 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in y around 0 35.4%

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

   if 4.1999999999999999e-69 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. distribute-lft-neg-out 55.9%

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

      3. *-commutative 55.9%

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

   4. Simplified 55.9%

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

   5. Taylor expanded in y around 0 22.3%

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

      1. mul-1-neg 22.3%

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

      2. unsub-neg 22.3%

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

      3. *-commutative 22.3%

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

   7. Simplified 22.3%

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

   8. Taylor expanded in y around inf 23.2%

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

      1. mul-1-neg 23.2%

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

      2. associate-*r* 26.5%

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

      3. *-commutative 26.5%

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

   10. Simplified 26.5%

       \[\leadsto \color{blue}{-y \cdot \left(t \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \]

Alternative 18: 28.5% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{+52}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.95e+52) (* (* x t) (- y)) (* x (- 1.0 (* y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.95e+52) {
		tmp = (x * t) * -y;
	} else {
		tmp = x * (1.0 - (y * t));
	}
	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 <= (-2.95d+52)) then
        tmp = (x * t) * -y
    else
        tmp = x * (1.0d0 - (y * t))
    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 <= -2.95e+52) {
		tmp = (x * t) * -y;
	} else {
		tmp = x * (1.0 - (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.95e+52:
		tmp = (x * t) * -y
	else:
		tmp = x * (1.0 - (y * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.95e+52)
		tmp = Float64(Float64(x * t) * Float64(-y));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.95e+52)
		tmp = (x * t) * -y;
	else
		tmp = x * (1.0 - (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.95e+52], N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.94999999999999998e52

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 30.0%

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

      1. mul-1-neg 30.0%

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

      2. distribute-lft-neg-out 30.0%

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

      3. *-commutative 30.0%

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

   4. Simplified 30.0%

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

   5. Taylor expanded in y around 0 12.7%

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

      1. mul-1-neg 12.7%

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

      2. unsub-neg 12.7%

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

      3. *-commutative 12.7%

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

   7. Simplified 12.7%

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

   8. Taylor expanded in y around inf 29.5%

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

      1. mul-1-neg 29.5%

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

      2. associate-*r* 32.7%

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

      3. *-commutative 32.7%

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

   10. Simplified 32.7%

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

   if -2.94999999999999998e52 < b

   1. Initial program 96.6%

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

   2. Taylor expanded in t around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. distribute-lft-neg-out 58.5%

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

      3. *-commutative 58.5%

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

   4. Simplified 58.5%

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

   5. Taylor expanded in y around 0 30.8%

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

      1. mul-1-neg 30.8%

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

      2. unsub-neg 30.8%

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

      3. *-commutative 30.8%

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

   7. Simplified 30.8%

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

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{+52}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \]

Alternative 19: 19.4% accurate, 315.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in t around inf 52.9%

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

   1. mul-1-neg 52.9%

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

   2. distribute-lft-neg-out 52.9%

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

   3. *-commutative 52.9%

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

4. Simplified 52.9%

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

5. Taylor expanded in y around 0 18.9%

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

6. Final simplification 18.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))