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

Percentage Accurate: 96.8% → 99.6%

Time: 21.0s

Alternatives: 22

Speedup: 1.0×

• 21.0% 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: 96.8% 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 95.8%

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

   1. +-commutative 95.8%

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

   2. fma-def 96.6%

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

   3. sub-neg 96.6%

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

   4. log1p-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 96.8% 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 95.8%

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

2. Final simplification 95.8%

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

Alternative 3: 86.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-28} \lor \neg \left(y \leq 2.35 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.4e-28) (not (<= y 2.35e-26)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (- z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.4e-28) || !(y <= 2.35e-26)) {
		tmp = x * exp((y * (log(z) - t)));
	} 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 <= (-2.4d-28)) .or. (.not. (y <= 2.35d-26))) then
        tmp = x * exp((y * (log(z) - t)))
    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 <= -2.4e-28) || !(y <= 2.35e-26)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * (-z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.4e-28) or not (y <= 2.35e-26):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * (-z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.4e-28) || !(y <= 2.35e-26))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	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 <= -2.4e-28) || ~((y <= 2.35e-26)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((a * (-z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.4e-28], N[Not[LessEqual[y, 2.35e-26]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $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 < -2.4000000000000002e-28 or 2.34999999999999995e-26 < y

   1. Initial program 96.4%

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

   2. Taylor expanded in y around inf 89.3%

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

   if -2.4000000000000002e-28 < y < 2.34999999999999995e-26

   1. Initial program 95.1%

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

   2. Taylor expanded in y around 0 85.9%

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

      1. sub-neg 85.9%

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

      2. neg-mul-1 85.9%

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

      3. log1p-def 91.6%

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

      4. neg-mul-1 91.6%

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

   4. Simplified 91.6%

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

   5. Taylor expanded in z around 0 91.6%

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

      1. associate-*r* 91.6%

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

      2. associate-*r* 91.6%

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

      3. distribute-lft-out 91.6%

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

      4. mul-1-neg 91.6%

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

      5. +-commutative 91.6%

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

   7. Simplified 91.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-28} \lor \neg \left(y \leq 2.35 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \]

Alternative 4: 74.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+19}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-26}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.2e+19)
   (* x (pow z y))
   (if (<= y 1.8e-26) (* x (exp (* a (- (- z) b)))) (* x (exp (* y (- t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.2e+19) {
		tmp = x * pow(z, y);
	} else if (y <= 1.8e-26) {
		tmp = x * exp((a * (-z - b)));
	} else {
		tmp = x * exp((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 (y <= (-9.2d+19)) then
        tmp = x * (z ** y)
    else if (y <= 1.8d-26) then
        tmp = x * exp((a * (-z - b)))
    else
        tmp = x * exp((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 (y <= -9.2e+19) {
		tmp = x * Math.pow(z, y);
	} else if (y <= 1.8e-26) {
		tmp = x * Math.exp((a * (-z - b)));
	} else {
		tmp = x * Math.exp((y * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.2e+19:
		tmp = x * math.pow(z, y)
	elif y <= 1.8e-26:
		tmp = x * math.exp((a * (-z - b)))
	else:
		tmp = x * math.exp((y * -t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.2e+19)
		tmp = Float64(x * (z ^ y));
	elseif (y <= 1.8e-26)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	else
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9.2e+19)
		tmp = x * (z ^ y);
	elseif (y <= 1.8e-26)
		tmp = x * exp((a * (-z - b)));
	else
		tmp = x * exp((y * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.2e+19], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-26], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.2e19

   1. Initial program 96.8%

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

   2. Taylor expanded in y around inf 90.5%

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

   3. Taylor expanded in t around 0 69.8%

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

      1. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   if -9.2e19 < y < 1.8000000000000001e-26

   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 y around 0 84.3%

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

      1. sub-neg 84.3%

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

      2. neg-mul-1 84.3%

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

      3. log1p-def 89.6%

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

      4. neg-mul-1 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in z around 0 89.6%

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

      1. associate-*r* 89.6%

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

      2. associate-*r* 89.6%

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

      3. distribute-lft-out 89.6%

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

      4. mul-1-neg 89.6%

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

      5. +-commutative 89.6%

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

   7. Simplified 89.6%

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

   if 1.8000000000000001e-26 < y

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. distribute-lft-neg-out 68.5%

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

      3. *-commutative 68.5%

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

   4. Simplified 68.5%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+19}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-26}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 5: 72.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+18} \lor \neg \left(y \leq 9.2 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.6e+18) (not (<= y 9.2e-26)))
   (* 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 <= -1.6e+18) || !(y <= 9.2e-26)) {
		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 <= (-1.6d+18)) .or. (.not. (y <= 9.2d-26))) 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 <= -1.6e+18) || !(y <= 9.2e-26)) {
		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 <= -1.6e+18) or not (y <= 9.2e-26):
		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 <= -1.6e+18) || !(y <= 9.2e-26))
		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 <= -1.6e+18) || ~((y <= 9.2e-26)))
		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, -1.6e+18], N[Not[LessEqual[y, 9.2e-26]], $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 < -1.6e18 or 9.20000000000000035e-26 < y

   1. Initial program 96.1%

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

   2. Taylor expanded in y around inf 89.9%

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

   3. Taylor expanded in t around 0 63.7%

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

      1. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   if -1.6e18 < y < 9.20000000000000035e-26

   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 b around inf 83.6%

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

      1. mul-1-neg 83.6%

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

      2. distribute-rgt-neg-out 83.6%

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

   4. Simplified 83.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+18} \lor \neg \left(y \leq 9.2 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 6: 69.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+92} \lor \neg \left(b \leq 5.8 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.5e+92) (not (<= b 5.8e+41)))
   (* x (exp (* a (- b))))
   (* x (exp (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.5e+92) || !(b <= 5.8e+41)) {
		tmp = x * exp((a * -b));
	} else {
		tmp = x * exp((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 <= (-2.5d+92)) .or. (.not. (b <= 5.8d+41))) then
        tmp = x * exp((a * -b))
    else
        tmp = x * exp((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 <= -2.5e+92) || !(b <= 5.8e+41)) {
		tmp = x * Math.exp((a * -b));
	} else {
		tmp = x * Math.exp((y * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.5e+92) or not (b <= 5.8e+41):
		tmp = x * math.exp((a * -b))
	else:
		tmp = x * math.exp((y * -t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.5e+92) || !(b <= 5.8e+41))
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	else
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.5e+92) || ~((b <= 5.8e+41)))
		tmp = x * exp((a * -b));
	else
		tmp = x * exp((y * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.5e+92], N[Not[LessEqual[b, 5.8e+41]], $MachinePrecision]], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.50000000000000011e92 or 5.79999999999999977e41 < b

   1. Initial program 96.2%

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

   2. Taylor expanded in b around inf 82.4%

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

      1. mul-1-neg 82.4%

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

      2. distribute-rgt-neg-out 82.4%

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

   4. Simplified 82.4%

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

   if -2.50000000000000011e92 < b < 5.79999999999999977e41

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf 73.6%

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

      1. mul-1-neg 73.6%

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

      2. distribute-lft-neg-out 73.6%

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

      3. *-commutative 73.6%

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

   4. Simplified 73.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+92} \lor \neg \left(b \leq 5.8 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 7: 55.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(1 + \left(0.5 \cdot \left(\left(t \cdot t\right) \cdot \left(y \cdot y\right)\right) - y \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -0.007:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.35e+83)
   (* x (+ 1.0 (- (* 0.5 (* (* t t) (* y y))) (* y t))))
   (if (<= t -0.007) (* a (* x (- z))) (* x (pow z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.35e+83) {
		tmp = x * (1.0 + ((0.5 * ((t * t) * (y * y))) - (y * t)));
	} else if (t <= -0.007) {
		tmp = a * (x * -z);
	} 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 <= (-1.35d+83)) then
        tmp = x * (1.0d0 + ((0.5d0 * ((t * t) * (y * y))) - (y * t)))
    else if (t <= (-0.007d0)) then
        tmp = a * (x * -z)
    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 <= -1.35e+83) {
		tmp = x * (1.0 + ((0.5 * ((t * t) * (y * y))) - (y * t)));
	} else if (t <= -0.007) {
		tmp = a * (x * -z);
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.35e+83:
		tmp = x * (1.0 + ((0.5 * ((t * t) * (y * y))) - (y * t)))
	elif t <= -0.007:
		tmp = a * (x * -z)
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.35e+83)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(0.5 * Float64(Float64(t * t) * Float64(y * y))) - Float64(y * t))));
	elseif (t <= -0.007)
		tmp = Float64(a * Float64(x * Float64(-z)));
	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 <= -1.35e+83)
		tmp = x * (1.0 + ((0.5 * ((t * t) * (y * y))) - (y * t)));
	elseif (t <= -0.007)
		tmp = a * (x * -z);
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.35e+83], N[(x * N[(1.0 + N[(N[(0.5 * N[(N[(t * t), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -0.007], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000003e83

   1. Initial program 96.1%

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

   2. Taylor expanded in t around inf 83.1%

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

      1. mul-1-neg 83.1%

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

      2. distribute-lft-neg-out 83.1%

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

      3. *-commutative 83.1%

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

   4. Simplified 83.1%

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

   5. Taylor expanded in y around 0 50.3%

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

      1. associate-+r+ 50.3%

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

      2. mul-1-neg 50.3%

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

      3. unsub-neg 50.3%

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

      4. *-commutative 50.3%

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

      5. associate-*r* 50.3%

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

      6. unpow2 50.3%

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

      7. *-commutative 50.3%

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

      8. unpow2 50.3%

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

   7. Simplified 50.3%

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

   8. Taylor expanded in x around 0 50.3%

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

      1. associate--l+ 50.3%

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

      2. unpow2 50.3%

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

      3. unpow2 50.3%

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

   10. Simplified 50.3%

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

   if -1.35000000000000003e83 < t < -0.00700000000000000015

   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 y around 0 63.0%

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

      1. sub-neg 63.0%

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

      2. neg-mul-1 63.0%

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

      3. log1p-def 63.0%

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

      4. neg-mul-1 63.0%

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

   4. Simplified 63.0%

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

   5. Taylor expanded in z around 0 63.0%

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

      1. associate-*r* 63.0%

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

      2. associate-*r* 63.0%

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

      3. distribute-lft-out 63.0%

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

      4. mul-1-neg 63.0%

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

      5. +-commutative 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in a around 0 10.3%

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

      1. mul-1-neg 10.3%

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

      2. unsub-neg 10.3%

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

      3. *-commutative 10.3%

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

      4. associate-*l* 10.8%

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

      5. *-commutative 10.8%

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

   10. Simplified 10.8%

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

   11. Taylor expanded in z around inf 54.8%

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

       1. mul-1-neg 54.8%

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

       2. distribute-rgt-neg-in 54.8%

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

   13. Simplified 54.8%

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

   if -0.00700000000000000015 < t

   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 y around inf 73.6%

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

   3. Taylor expanded in t around 0 64.0%

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

      1. *-commutative 64.0%

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

   5. Simplified 64.0%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(1 + \left(0.5 \cdot \left(\left(t \cdot t\right) \cdot \left(y \cdot y\right)\right) - y \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -0.007:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 8: 43.7% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \left(a \cdot a\right)\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \left(1 + \left(0.5 \cdot \left(\left(t \cdot t\right) \cdot \left(y \cdot y\right)\right) - y \cdot t\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 + \left(t_1 \cdot \left(b \cdot b\right) - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 0.5 (* a a))))
   (if (<= y -4.3e-169)
     (* x (+ 1.0 (- (* 0.5 (* (* t t) (* y y))) (* y t))))
     (if (<= y 1.75e-19)
       (* x (+ 1.0 (- (* t_1 (* b b)) (* a b))))
       (* t_1 (* x (* b b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (a * a);
	double tmp;
	if (y <= -4.3e-169) {
		tmp = x * (1.0 + ((0.5 * ((t * t) * (y * y))) - (y * t)));
	} else if (y <= 1.75e-19) {
		tmp = x * (1.0 + ((t_1 * (b * b)) - (a * b)));
	} else {
		tmp = t_1 * (x * (b * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * (a * a)
    if (y <= (-4.3d-169)) then
        tmp = x * (1.0d0 + ((0.5d0 * ((t * t) * (y * y))) - (y * t)))
    else if (y <= 1.75d-19) then
        tmp = x * (1.0d0 + ((t_1 * (b * b)) - (a * b)))
    else
        tmp = t_1 * (x * (b * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (a * a);
	double tmp;
	if (y <= -4.3e-169) {
		tmp = x * (1.0 + ((0.5 * ((t * t) * (y * y))) - (y * t)));
	} else if (y <= 1.75e-19) {
		tmp = x * (1.0 + ((t_1 * (b * b)) - (a * b)));
	} else {
		tmp = t_1 * (x * (b * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.5 * (a * a)
	tmp = 0
	if y <= -4.3e-169:
		tmp = x * (1.0 + ((0.5 * ((t * t) * (y * y))) - (y * t)))
	elif y <= 1.75e-19:
		tmp = x * (1.0 + ((t_1 * (b * b)) - (a * b)))
	else:
		tmp = t_1 * (x * (b * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.5 * Float64(a * a))
	tmp = 0.0
	if (y <= -4.3e-169)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(0.5 * Float64(Float64(t * t) * Float64(y * y))) - Float64(y * t))));
	elseif (y <= 1.75e-19)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(t_1 * Float64(b * b)) - Float64(a * b))));
	else
		tmp = Float64(t_1 * Float64(x * Float64(b * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.5 * (a * a);
	tmp = 0.0;
	if (y <= -4.3e-169)
		tmp = x * (1.0 + ((0.5 * ((t * t) * (y * y))) - (y * t)));
	elseif (y <= 1.75e-19)
		tmp = x * (1.0 + ((t_1 * (b * b)) - (a * b)));
	else
		tmp = t_1 * (x * (b * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e-169], N[(x * N[(1.0 + N[(N[(0.5 * N[(N[(t * t), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-19], N[(x * N[(1.0 + N[(N[(t$95$1 * N[(b * b), $MachinePrecision]), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.29999999999999984e-169

   1. Initial program 97.0%

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

   2. Taylor expanded in t around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. distribute-lft-neg-out 64.3%

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

      3. *-commutative 64.3%

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

   4. Simplified 64.3%

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

   5. Taylor expanded in y around 0 41.0%

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

      1. associate-+r+ 41.0%

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

      2. mul-1-neg 41.0%

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

      3. unsub-neg 41.0%

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

      4. *-commutative 41.0%

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

      5. associate-*r* 41.0%

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

      6. unpow2 41.0%

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

      7. *-commutative 41.0%

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

      8. unpow2 41.0%

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

   7. Simplified 41.0%

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

   8. Taylor expanded in x around 0 43.2%

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

      1. associate--l+ 43.2%

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

      2. unpow2 43.2%

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

      3. unpow2 43.2%

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

   10. Simplified 43.2%

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

   if -4.29999999999999984e-169 < y < 1.75000000000000008e-19

   1. Initial program 94.7%

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

   2. Taylor expanded in b around inf 88.1%

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

      1. mul-1-neg 88.1%

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

      2. distribute-rgt-neg-out 88.1%

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

   4. Simplified 88.1%

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

   5. Taylor expanded in a around 0 52.2%

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

      1. associate-+r+ 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. *-commutative 52.2%

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

      5. associate-*r* 57.4%

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

      6. unpow2 57.4%

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

      7. unpow2 57.4%

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

      8. unswap-sqr 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in x around 0 59.4%

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

      1. associate--l+ 59.4%

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

      2. associate-*r* 59.4%

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

      3. unpow2 59.4%

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

      4. unpow2 59.4%

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

   10. Simplified 59.4%

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

   if 1.75000000000000008e-19 < y

   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 b around inf 42.7%

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

      1. mul-1-neg 42.7%

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

      2. distribute-rgt-neg-out 42.7%

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

   4. Simplified 42.7%

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

   5. Taylor expanded in a around 0 21.8%

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

      1. associate-+r+ 21.8%

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

      2. mul-1-neg 21.8%

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

      3. unsub-neg 21.8%

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

      4. *-commutative 21.8%

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

      5. associate-*r* 23.4%

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

      6. unpow2 23.4%

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

      7. unpow2 23.4%

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

      8. unswap-sqr 19.3%

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

   7. Simplified 19.3%

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

   8. Taylor expanded in a around inf 40.0%

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

      1. associate-*r* 40.0%

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

      2. unpow2 40.0%

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

      3. *-commutative 40.0%

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

      4. unpow2 40.0%

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

   10. Simplified 40.0%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \left(1 + \left(0.5 \cdot \left(\left(t \cdot t\right) \cdot \left(y \cdot y\right)\right) - y \cdot t\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 + \left(\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(b \cdot b\right) - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \end{array} \]

Alternative 9: 46.1% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \left(a \cdot a\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-105}:\\ \;\;\;\;\left(x - y \cdot \left(x \cdot t\right)\right) + 0.5 \cdot \left(t \cdot \left(t \cdot \left(x \cdot \left(y \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(1 + \left(t_1 \cdot \left(b \cdot b\right) - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 0.5 (* a a))))
   (if (<= y -5.8e-105)
     (+ (- x (* y (* x t))) (* 0.5 (* t (* t (* x (* y y))))))
     (if (<= y 2.05e-20)
       (* x (+ 1.0 (- (* t_1 (* b b)) (* a b))))
       (* t_1 (* x (* b b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (a * a);
	double tmp;
	if (y <= -5.8e-105) {
		tmp = (x - (y * (x * t))) + (0.5 * (t * (t * (x * (y * y)))));
	} else if (y <= 2.05e-20) {
		tmp = x * (1.0 + ((t_1 * (b * b)) - (a * b)));
	} else {
		tmp = t_1 * (x * (b * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * (a * a)
    if (y <= (-5.8d-105)) then
        tmp = (x - (y * (x * t))) + (0.5d0 * (t * (t * (x * (y * y)))))
    else if (y <= 2.05d-20) then
        tmp = x * (1.0d0 + ((t_1 * (b * b)) - (a * b)))
    else
        tmp = t_1 * (x * (b * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (a * a);
	double tmp;
	if (y <= -5.8e-105) {
		tmp = (x - (y * (x * t))) + (0.5 * (t * (t * (x * (y * y)))));
	} else if (y <= 2.05e-20) {
		tmp = x * (1.0 + ((t_1 * (b * b)) - (a * b)));
	} else {
		tmp = t_1 * (x * (b * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.5 * (a * a)
	tmp = 0
	if y <= -5.8e-105:
		tmp = (x - (y * (x * t))) + (0.5 * (t * (t * (x * (y * y)))))
	elif y <= 2.05e-20:
		tmp = x * (1.0 + ((t_1 * (b * b)) - (a * b)))
	else:
		tmp = t_1 * (x * (b * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.5 * Float64(a * a))
	tmp = 0.0
	if (y <= -5.8e-105)
		tmp = Float64(Float64(x - Float64(y * Float64(x * t))) + Float64(0.5 * Float64(t * Float64(t * Float64(x * Float64(y * y))))));
	elseif (y <= 2.05e-20)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(t_1 * Float64(b * b)) - Float64(a * b))));
	else
		tmp = Float64(t_1 * Float64(x * Float64(b * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.5 * (a * a);
	tmp = 0.0;
	if (y <= -5.8e-105)
		tmp = (x - (y * (x * t))) + (0.5 * (t * (t * (x * (y * y)))));
	elseif (y <= 2.05e-20)
		tmp = x * (1.0 + ((t_1 * (b * b)) - (a * b)));
	else
		tmp = t_1 * (x * (b * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e-105], N[(N[(x - N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(t * N[(t * N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-20], N[(x * N[(1.0 + N[(N[(t$95$1 * N[(b * b), $MachinePrecision]), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.80000000000000007e-105

   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 t around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. distribute-lft-neg-out 62.8%

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

      3. *-commutative 62.8%

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

   4. Simplified 62.8%

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

   5. Taylor expanded in y around 0 38.3%

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

      1. associate-+r+ 38.3%

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

      2. mul-1-neg 38.3%

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

      3. unsub-neg 38.3%

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

      4. *-commutative 38.3%

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

      5. associate-*r* 38.3%

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

      6. unpow2 38.3%

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

      7. *-commutative 38.3%

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

      8. unpow2 38.3%

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

   7. Simplified 38.3%

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

   8. Taylor expanded in t around 0 38.3%

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

      1. associate-+r+ 38.3%

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

      2. mul-1-neg 38.3%

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

      3. sub-neg 38.3%

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

      4. associate-*r* 42.0%

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

      5. unpow2 42.0%

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

      6. unpow2 42.0%

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

      7. associate-*l* 47.2%

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

   10. Simplified 47.2%

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

   if -5.80000000000000007e-105 < y < 2.05e-20

   1. Initial program 94.7%

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

   2. Taylor expanded in b around inf 85.6%

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

      1. mul-1-neg 85.6%

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

      2. distribute-rgt-neg-out 85.6%

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

   4. Simplified 85.6%

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

   5. Taylor expanded in a around 0 52.4%

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

      1. associate-+r+ 52.4%

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

      2. mul-1-neg 52.4%

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

      3. unsub-neg 52.4%

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

      4. *-commutative 52.4%

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

      5. associate-*r* 57.7%

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

      6. unpow2 57.7%

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

      7. unpow2 57.7%

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

      8. unswap-sqr 57.4%

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

   7. Simplified 57.4%

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

   8. Taylor expanded in x around 0 59.5%

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

      1. associate--l+ 59.5%

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

      2. associate-*r* 59.5%

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

      3. unpow2 59.5%

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

      4. unpow2 59.5%

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

   10. Simplified 59.5%

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

   if 2.05e-20 < y

   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 b around inf 42.7%

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

      1. mul-1-neg 42.7%

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

      2. distribute-rgt-neg-out 42.7%

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

   4. Simplified 42.7%

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

   5. Taylor expanded in a around 0 21.8%

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

      1. associate-+r+ 21.8%

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

      2. mul-1-neg 21.8%

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

      3. unsub-neg 21.8%

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

      4. *-commutative 21.8%

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

      5. associate-*r* 23.4%

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

      6. unpow2 23.4%

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

      7. unpow2 23.4%

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

      8. unswap-sqr 19.3%

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

   7. Simplified 19.3%

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

   8. Taylor expanded in a around inf 40.0%

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

      1. associate-*r* 40.0%

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

      2. unpow2 40.0%

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

      3. *-commutative 40.0%

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

      4. unpow2 40.0%

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

   10. Simplified 40.0%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-105}:\\ \;\;\;\;\left(x - y \cdot \left(x \cdot t\right)\right) + 0.5 \cdot \left(t \cdot \left(t \cdot \left(x \cdot \left(y \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(1 + \left(\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(b \cdot b\right) - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \end{array} \]

Alternative 10: 42.1% accurate, 16.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(1 + \left(0.5 \cdot \left(\left(t \cdot t\right) \cdot \left(y \cdot y\right)\right) - y \cdot t\right)\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-20}:\\ \;\;\;\;x - x \cdot \left(a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.1e-162)
   (* x (+ 1.0 (- (* 0.5 (* (* t t) (* y y))) (* y t))))
   (if (<= y 2.65e-20)
     (- x (* x (* a (+ z b))))
     (* (* 0.5 (* a a)) (* x (* b b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.1e-162) {
		tmp = x * (1.0 + ((0.5 * ((t * t) * (y * y))) - (y * t)));
	} else if (y <= 2.65e-20) {
		tmp = x - (x * (a * (z + b)));
	} else {
		tmp = (0.5 * (a * a)) * (x * (b * 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 <= (-4.1d-162)) then
        tmp = x * (1.0d0 + ((0.5d0 * ((t * t) * (y * y))) - (y * t)))
    else if (y <= 2.65d-20) then
        tmp = x - (x * (a * (z + b)))
    else
        tmp = (0.5d0 * (a * a)) * (x * (b * 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 <= -4.1e-162) {
		tmp = x * (1.0 + ((0.5 * ((t * t) * (y * y))) - (y * t)));
	} else if (y <= 2.65e-20) {
		tmp = x - (x * (a * (z + b)));
	} else {
		tmp = (0.5 * (a * a)) * (x * (b * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.1e-162:
		tmp = x * (1.0 + ((0.5 * ((t * t) * (y * y))) - (y * t)))
	elif y <= 2.65e-20:
		tmp = x - (x * (a * (z + b)))
	else:
		tmp = (0.5 * (a * a)) * (x * (b * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.1e-162)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(0.5 * Float64(Float64(t * t) * Float64(y * y))) - Float64(y * t))));
	elseif (y <= 2.65e-20)
		tmp = Float64(x - Float64(x * Float64(a * Float64(z + b))));
	else
		tmp = Float64(Float64(0.5 * Float64(a * a)) * Float64(x * Float64(b * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.1e-162)
		tmp = x * (1.0 + ((0.5 * ((t * t) * (y * y))) - (y * t)));
	elseif (y <= 2.65e-20)
		tmp = x - (x * (a * (z + b)));
	else
		tmp = (0.5 * (a * a)) * (x * (b * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.1e-162], N[(x * N[(1.0 + N[(N[(0.5 * N[(N[(t * t), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e-20], N[(x - N[(x * N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision] * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.10000000000000019e-162

   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 64.9%

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

      1. mul-1-neg 64.9%

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

      2. distribute-lft-neg-out 64.9%

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

      3. *-commutative 64.9%

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

   4. Simplified 64.9%

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

   5. Taylor expanded in y around 0 41.4%

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

      1. associate-+r+ 41.4%

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

      2. mul-1-neg 41.4%

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

      3. unsub-neg 41.4%

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

      4. *-commutative 41.4%

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

      5. associate-*r* 41.4%

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

      6. unpow2 41.4%

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

      7. *-commutative 41.4%

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

      8. unpow2 41.4%

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

   7. Simplified 41.4%

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

   8. Taylor expanded in x around 0 43.6%

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

      1. associate--l+ 43.6%

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

      2. unpow2 43.6%

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

      3. unpow2 43.6%

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

   10. Simplified 43.6%

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

   if -4.10000000000000019e-162 < y < 2.6500000000000001e-20

   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 89.3%

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

      1. sub-neg 89.3%

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

      2. neg-mul-1 89.3%

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

      3. log1p-def 94.5%

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

      4. neg-mul-1 94.5%

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

   4. Simplified 94.5%

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

   5. Taylor expanded in z around 0 94.5%

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

      1. associate-*r* 94.5%

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

      2. associate-*r* 94.5%

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

      3. distribute-lft-out 94.5%

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

      4. mul-1-neg 94.5%

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

      5. +-commutative 94.5%

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

   7. Simplified 94.5%

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

   8. Taylor expanded in a around 0 47.6%

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

      1. mul-1-neg 47.6%

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

      2. unsub-neg 47.6%

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

      3. *-commutative 47.6%

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

      4. associate-*l* 53.3%

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

      5. *-commutative 53.3%

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

   10. Simplified 53.3%

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

   if 2.6500000000000001e-20 < y

   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 b around inf 42.7%

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

      1. mul-1-neg 42.7%

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

      2. distribute-rgt-neg-out 42.7%

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

   4. Simplified 42.7%

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

   5. Taylor expanded in a around 0 21.8%

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

      1. associate-+r+ 21.8%

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

      2. mul-1-neg 21.8%

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

      3. unsub-neg 21.8%

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

      4. *-commutative 21.8%

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

      5. associate-*r* 23.4%

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

      6. unpow2 23.4%

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

      7. unpow2 23.4%

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

      8. unswap-sqr 19.3%

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

   7. Simplified 19.3%

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

   8. Taylor expanded in a around inf 40.0%

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

      1. associate-*r* 40.0%

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

      2. unpow2 40.0%

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

      3. *-commutative 40.0%

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

      4. unpow2 40.0%

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

   10. Simplified 40.0%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(1 + \left(0.5 \cdot \left(\left(t \cdot t\right) \cdot \left(y \cdot y\right)\right) - y \cdot t\right)\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-20}:\\ \;\;\;\;x - x \cdot \left(a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \end{array} \]

Alternative 11: 33.4% accurate, 18.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \mathbf{if}\;a \leq -1.06 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+238}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* 0.5 (* a a)) (* x (* b b)))))
   (if (<= a -1.06e-59)
     t_1
     (if (<= a 3.5e+119)
       (* x (- 1.0 (* y t)))
       (if (<= a 4.2e+238) t_1 (* t (* x (- y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.5 * (a * a)) * (x * (b * b));
	double tmp;
	if (a <= -1.06e-59) {
		tmp = t_1;
	} else if (a <= 3.5e+119) {
		tmp = x * (1.0 - (y * t));
	} else if (a <= 4.2e+238) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (0.5d0 * (a * a)) * (x * (b * b))
    if (a <= (-1.06d-59)) then
        tmp = t_1
    else if (a <= 3.5d+119) then
        tmp = x * (1.0d0 - (y * t))
    else if (a <= 4.2d+238) then
        tmp = t_1
    else
        tmp = 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 t_1 = (0.5 * (a * a)) * (x * (b * b));
	double tmp;
	if (a <= -1.06e-59) {
		tmp = t_1;
	} else if (a <= 3.5e+119) {
		tmp = x * (1.0 - (y * t));
	} else if (a <= 4.2e+238) {
		tmp = t_1;
	} else {
		tmp = t * (x * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (0.5 * (a * a)) * (x * (b * b))
	tmp = 0
	if a <= -1.06e-59:
		tmp = t_1
	elif a <= 3.5e+119:
		tmp = x * (1.0 - (y * t))
	elif a <= 4.2e+238:
		tmp = t_1
	else:
		tmp = t * (x * -y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(0.5 * Float64(a * a)) * Float64(x * Float64(b * b)))
	tmp = 0.0
	if (a <= -1.06e-59)
		tmp = t_1;
	elseif (a <= 3.5e+119)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif (a <= 4.2e+238)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(x * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (0.5 * (a * a)) * (x * (b * b));
	tmp = 0.0;
	if (a <= -1.06e-59)
		tmp = t_1;
	elseif (a <= 3.5e+119)
		tmp = x * (1.0 - (y * t));
	elseif (a <= 4.2e+238)
		tmp = t_1;
	else
		tmp = t * (x * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision] * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.06e-59], t$95$1, If[LessEqual[a, 3.5e+119], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+238], t$95$1, N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.06e-59 or 3.5000000000000001e119 < a < 4.20000000000000015e238

   1. Initial program 93.3%

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

   2. Taylor expanded in b around inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. distribute-rgt-neg-out 69.8%

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

   4. Simplified 69.8%

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

   5. Taylor expanded in a around 0 37.1%

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

      1. associate-+r+ 37.1%

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

      2. mul-1-neg 37.1%

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

      3. unsub-neg 37.1%

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

      4. *-commutative 37.1%

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

      5. associate-*r* 41.9%

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

      6. unpow2 41.9%

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

      7. unpow2 41.9%

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

      8. unswap-sqr 37.5%

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

   7. Simplified 37.5%

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

   8. Taylor expanded in a around inf 40.1%

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

      1. associate-*r* 40.1%

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

      2. unpow2 40.1%

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

      3. *-commutative 40.1%

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

      4. unpow2 40.1%

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

   10. Simplified 40.1%

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

   if -1.06e-59 < a < 3.5000000000000001e119

   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 71.6%

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

      1. mul-1-neg 71.6%

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

      2. distribute-lft-neg-out 71.6%

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

      3. *-commutative 71.6%

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

   4. Simplified 71.6%

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

   5. Taylor expanded in y around 0 45.7%

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

      1. mul-1-neg 45.7%

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

      2. unsub-neg 45.7%

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

      3. *-commutative 45.7%

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

   7. Simplified 45.7%

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

   if 4.20000000000000015e238 < a

   1. Initial program 80.5%

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

   2. Taylor expanded in t around inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. distribute-lft-neg-out 48.6%

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

      3. *-commutative 48.6%

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

   4. Simplified 48.6%

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

   5. Taylor expanded in y around 0 16.4%

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

      1. mul-1-neg 16.4%

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

      2. unsub-neg 16.4%

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

      3. *-commutative 16.4%

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

   7. Simplified 16.4%

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

   8. Taylor expanded in y around inf 54.7%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-59}:\\ \;\;\;\;\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+238}:\\ \;\;\;\;\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 12: 29.6% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+244}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.32e+244)
   (* x (* a (- b)))
   (if (<= a -1.65e+94)
     (* x (* y (- t)))
     (if (<= a -1.05e+53)
       (* a (* x (- z)))
       (if (<= a 6.2e+97) (* x (- 1.0 (* y t))) (* t (* x (- y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.32e+244) {
		tmp = x * (a * -b);
	} else if (a <= -1.65e+94) {
		tmp = x * (y * -t);
	} else if (a <= -1.05e+53) {
		tmp = a * (x * -z);
	} else if (a <= 6.2e+97) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = 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 (a <= (-1.32d+244)) then
        tmp = x * (a * -b)
    else if (a <= (-1.65d+94)) then
        tmp = x * (y * -t)
    else if (a <= (-1.05d+53)) then
        tmp = a * (x * -z)
    else if (a <= 6.2d+97) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = 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 (a <= -1.32e+244) {
		tmp = x * (a * -b);
	} else if (a <= -1.65e+94) {
		tmp = x * (y * -t);
	} else if (a <= -1.05e+53) {
		tmp = a * (x * -z);
	} else if (a <= 6.2e+97) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = t * (x * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.32e+244:
		tmp = x * (a * -b)
	elif a <= -1.65e+94:
		tmp = x * (y * -t)
	elif a <= -1.05e+53:
		tmp = a * (x * -z)
	elif a <= 6.2e+97:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = t * (x * -y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.32e+244)
		tmp = Float64(x * Float64(a * Float64(-b)));
	elseif (a <= -1.65e+94)
		tmp = Float64(x * Float64(y * Float64(-t)));
	elseif (a <= -1.05e+53)
		tmp = Float64(a * Float64(x * Float64(-z)));
	elseif (a <= 6.2e+97)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(t * Float64(x * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.32e+244)
		tmp = x * (a * -b);
	elseif (a <= -1.65e+94)
		tmp = x * (y * -t);
	elseif (a <= -1.05e+53)
		tmp = a * (x * -z);
	elseif (a <= 6.2e+97)
		tmp = x * (1.0 - (y * t));
	else
		tmp = t * (x * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.32e+244], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.65e+94], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.05e+53], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+97], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.31999999999999998e244

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 93.0%

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

      1. sub-neg 93.0%

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

      2. neg-mul-1 93.0%

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

      3. log1p-def 93.0%

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

      4. neg-mul-1 93.0%

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

   4. Simplified 93.0%

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

   5. Taylor expanded in z around 0 93.0%

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

      1. associate-*r* 93.0%

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

      2. associate-*r* 93.0%

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

      3. distribute-lft-out 93.0%

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

      4. mul-1-neg 93.0%

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

      5. +-commutative 93.0%

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

   7. Simplified 93.0%

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

   8. Taylor expanded in a around 0 44.2%

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

      1. mul-1-neg 44.2%

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

      2. unsub-neg 44.2%

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

      3. *-commutative 44.2%

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

      4. associate-*l* 50.8%

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

      5. *-commutative 50.8%

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

   10. Simplified 50.8%

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

   11. Taylor expanded in b around inf 37.1%

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

       1. mul-1-neg 37.1%

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

       2. associate-*r* 43.6%

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

       3. distribute-rgt-neg-in 43.6%

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

   13. Simplified 43.6%

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

   if -1.31999999999999998e244 < a < -1.65e94

   1. Initial program 91.0%

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

   2. Taylor expanded in t around inf 52.8%

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

      1. mul-1-neg 52.8%

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

      2. distribute-lft-neg-out 52.8%

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

      3. *-commutative 52.8%

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

   4. Simplified 52.8%

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

   5. Taylor expanded in y around 0 17.4%

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

      1. mul-1-neg 17.4%

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

      2. unsub-neg 17.4%

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

      3. *-commutative 17.4%

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

   7. Simplified 17.4%

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

   8. Taylor expanded in y around inf 28.7%

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

      1. mul-1-neg 28.7%

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

      2. distribute-rgt-neg-in 28.7%

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

   10. Simplified 28.7%

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

   if -1.65e94 < a < -1.0500000000000001e53

   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 y around 0 64.7%

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

      1. sub-neg 64.7%

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

      2. neg-mul-1 64.7%

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

      3. log1p-def 64.7%

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

      4. neg-mul-1 64.7%

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

   4. Simplified 64.7%

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

   5. Taylor expanded in z around 0 64.7%

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

      1. associate-*r* 64.7%

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

      2. associate-*r* 64.7%

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

      3. distribute-lft-out 64.7%

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

      4. mul-1-neg 64.7%

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

      5. +-commutative 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in a around 0 3.7%

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

      1. mul-1-neg 3.7%

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

      2. unsub-neg 3.7%

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

      3. *-commutative 3.7%

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

      4. associate-*l* 3.7%

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

      5. *-commutative 3.7%

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

   10. Simplified 3.7%

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

   11. Taylor expanded in z around inf 38.5%

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

       1. mul-1-neg 38.5%

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

       2. distribute-rgt-neg-in 38.5%

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

   13. Simplified 38.5%

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

   if -1.0500000000000001e53 < a < 6.19999999999999962e97

   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 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-lft-neg-out 70.8%

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

      3. *-commutative 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in y around 0 43.3%

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

      1. mul-1-neg 43.3%

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

      2. unsub-neg 43.3%

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

      3. *-commutative 43.3%

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

   7. Simplified 43.3%

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

   if 6.19999999999999962e97 < a

   1. Initial program 85.4%

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

   2. Taylor expanded in t around inf 47.2%

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

      1. mul-1-neg 47.2%

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

      2. distribute-lft-neg-out 47.2%

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

      3. *-commutative 47.2%

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

   4. Simplified 47.2%

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

   5. Taylor expanded in y around 0 17.9%

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

      1. mul-1-neg 17.9%

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

      2. unsub-neg 17.9%

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

      3. *-commutative 17.9%

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

   7. Simplified 17.9%

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

   8. Taylor expanded in y around inf 36.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+244}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 13: 27.0% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.45 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* x (- y)))))
   (if (<= y -1.9e-8)
     t_1
     (if (<= y 5.45e-219)
       x
       (if (<= y 5e-183) t_1 (if (<= y 1.16e-35) x (* y (* x (- t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (x * -y);
	double tmp;
	if (y <= -1.9e-8) {
		tmp = t_1;
	} else if (y <= 5.45e-219) {
		tmp = x;
	} else if (y <= 5e-183) {
		tmp = t_1;
	} else if (y <= 1.16e-35) {
		tmp = x;
	} else {
		tmp = y * (x * -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 * (x * -y)
    if (y <= (-1.9d-8)) then
        tmp = t_1
    else if (y <= 5.45d-219) then
        tmp = x
    else if (y <= 5d-183) then
        tmp = t_1
    else if (y <= 1.16d-35) then
        tmp = x
    else
        tmp = y * (x * -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 * (x * -y);
	double tmp;
	if (y <= -1.9e-8) {
		tmp = t_1;
	} else if (y <= 5.45e-219) {
		tmp = x;
	} else if (y <= 5e-183) {
		tmp = t_1;
	} else if (y <= 1.16e-35) {
		tmp = x;
	} else {
		tmp = y * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (x * -y)
	tmp = 0
	if y <= -1.9e-8:
		tmp = t_1
	elif y <= 5.45e-219:
		tmp = x
	elif y <= 5e-183:
		tmp = t_1
	elif y <= 1.16e-35:
		tmp = x
	else:
		tmp = y * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(x * Float64(-y)))
	tmp = 0.0
	if (y <= -1.9e-8)
		tmp = t_1;
	elseif (y <= 5.45e-219)
		tmp = x;
	elseif (y <= 5e-183)
		tmp = t_1;
	elseif (y <= 1.16e-35)
		tmp = x;
	else
		tmp = Float64(y * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (x * -y);
	tmp = 0.0;
	if (y <= -1.9e-8)
		tmp = t_1;
	elseif (y <= 5.45e-219)
		tmp = x;
	elseif (y <= 5e-183)
		tmp = t_1;
	elseif (y <= 1.16e-35)
		tmp = x;
	else
		tmp = y * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e-8], t$95$1, If[LessEqual[y, 5.45e-219], x, If[LessEqual[y, 5e-183], t$95$1, If[LessEqual[y, 1.16e-35], x, N[(y * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.90000000000000014e-8 or 5.4499999999999997e-219 < y < 5.0000000000000002e-183

   1. Initial program 93.6%

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

   2. Taylor expanded in t around inf 54.8%

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

      1. mul-1-neg 54.8%

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

      2. distribute-lft-neg-out 54.8%

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

      3. *-commutative 54.8%

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

   4. Simplified 54.8%

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

   5. Taylor expanded in y around 0 19.5%

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

      1. mul-1-neg 19.5%

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

      2. unsub-neg 19.5%

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

      3. *-commutative 19.5%

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

   7. Simplified 19.5%

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

   8. Taylor expanded in y around inf 27.7%

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

   if -1.90000000000000014e-8 < y < 5.4499999999999997e-219 or 5.0000000000000002e-183 < y < 1.16000000000000005e-35

   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 64.9%

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

   3. Taylor expanded in y around 0 43.0%

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

   if 1.16000000000000005e-35 < y

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. distribute-lft-neg-out 67.6%

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

      3. *-commutative 67.6%

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

   4. Simplified 67.6%

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

   5. Taylor expanded in y around 0 26.4%

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

      1. mul-1-neg 26.4%

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

      2. unsub-neg 26.4%

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

      3. *-commutative 26.4%

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

   7. Simplified 26.4%

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

   8. Taylor expanded in y around inf 26.7%

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

      1. mul-1-neg 26.7%

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

      2. associate-*r* 36.7%

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

      3. distribute-lft-neg-in 36.7%

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

      4. *-commutative 36.7%

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

   10. Simplified 36.7%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 5.45 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 14: 32.3% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00023:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-35}:\\ \;\;\;\;x - x \cdot \left(a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -0.00023)
   (* t (* x (- y)))
   (if (<= y 5.5e-35) (- x (* x (* a (+ z b)))) (* y (* x (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -0.00023) {
		tmp = t * (x * -y);
	} else if (y <= 5.5e-35) {
		tmp = x - (x * (a * (z + b)));
	} else {
		tmp = y * (x * -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 (y <= (-0.00023d0)) then
        tmp = t * (x * -y)
    else if (y <= 5.5d-35) then
        tmp = x - (x * (a * (z + b)))
    else
        tmp = y * (x * -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 (y <= -0.00023) {
		tmp = t * (x * -y);
	} else if (y <= 5.5e-35) {
		tmp = x - (x * (a * (z + b)));
	} else {
		tmp = y * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -0.00023:
		tmp = t * (x * -y)
	elif y <= 5.5e-35:
		tmp = x - (x * (a * (z + b)))
	else:
		tmp = y * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -0.00023)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 5.5e-35)
		tmp = Float64(x - Float64(x * Float64(a * Float64(z + b))));
	else
		tmp = Float64(y * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -0.00023)
		tmp = t * (x * -y);
	elseif (y <= 5.5e-35)
		tmp = x - (x * (a * (z + b)));
	else
		tmp = y * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -0.00023], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-35], N[(x - N[(x * N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3000000000000001e-4

   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 59.8%

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

      1. mul-1-neg 59.8%

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

      2. distribute-lft-neg-out 59.8%

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

      3. *-commutative 59.8%

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

   4. Simplified 59.8%

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

   5. Taylor expanded in y around 0 21.0%

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

      1. mul-1-neg 21.0%

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

      2. unsub-neg 21.0%

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

      3. *-commutative 21.0%

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

   7. Simplified 21.0%

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

   8. Taylor expanded in y around inf 23.4%

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

   if -2.3000000000000001e-4 < y < 5.4999999999999997e-35

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0 84.6%

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

      1. sub-neg 84.6%

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

      2. neg-mul-1 84.6%

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

      3. log1p-def 90.1%

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

      4. neg-mul-1 90.1%

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

   4. Simplified 90.1%

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

   5. Taylor expanded in z around 0 90.1%

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

      1. associate-*r* 90.1%

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

      2. associate-*r* 90.1%

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

      3. distribute-lft-out 90.1%

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

      4. mul-1-neg 90.1%

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

      5. +-commutative 90.1%

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

   7. Simplified 90.1%

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

   8. Taylor expanded in a around 0 46.3%

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

      1. mul-1-neg 46.3%

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

      2. unsub-neg 46.3%

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

      3. *-commutative 46.3%

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

      4. associate-*l* 52.1%

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

      5. *-commutative 52.1%

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

   10. Simplified 52.1%

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

   if 5.4999999999999997e-35 < y

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. distribute-lft-neg-out 67.6%

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

      3. *-commutative 67.6%

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

   4. Simplified 67.6%

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

   5. Taylor expanded in y around 0 26.4%

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

      1. mul-1-neg 26.4%

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

      2. unsub-neg 26.4%

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

      3. *-commutative 26.4%

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

   7. Simplified 26.4%

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

   8. Taylor expanded in y around inf 26.7%

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

      1. mul-1-neg 26.7%

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

      2. associate-*r* 36.7%

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

      3. distribute-lft-neg-in 36.7%

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

      4. *-commutative 36.7%

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

   10. Simplified 36.7%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00023:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-35}:\\ \;\;\;\;x - x \cdot \left(a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 15: 31.1% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-35}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.55e-5)
   (* t (* x (- y)))
   (if (<= y 5.5e-35) (- x (* a (* x b))) (* y (* x (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.55e-5) {
		tmp = t * (x * -y);
	} else if (y <= 5.5e-35) {
		tmp = x - (a * (x * b));
	} else {
		tmp = y * (x * -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 (y <= (-1.55d-5)) then
        tmp = t * (x * -y)
    else if (y <= 5.5d-35) then
        tmp = x - (a * (x * b))
    else
        tmp = y * (x * -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 (y <= -1.55e-5) {
		tmp = t * (x * -y);
	} else if (y <= 5.5e-35) {
		tmp = x - (a * (x * b));
	} else {
		tmp = y * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.55e-5:
		tmp = t * (x * -y)
	elif y <= 5.5e-35:
		tmp = x - (a * (x * b))
	else:
		tmp = y * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.55e-5)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 5.5e-35)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	else
		tmp = Float64(y * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.55e-5)
		tmp = t * (x * -y);
	elseif (y <= 5.5e-35)
		tmp = x - (a * (x * b));
	else
		tmp = y * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.55e-5], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-35], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55000000000000007e-5

   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 59.8%

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

      1. mul-1-neg 59.8%

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

      2. distribute-lft-neg-out 59.8%

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

      3. *-commutative 59.8%

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

   4. Simplified 59.8%

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

   5. Taylor expanded in y around 0 21.0%

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

      1. mul-1-neg 21.0%

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

      2. unsub-neg 21.0%

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

      3. *-commutative 21.0%

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

   7. Simplified 21.0%

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

   8. Taylor expanded in y around inf 23.4%

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

   if -1.55000000000000007e-5 < y < 5.4999999999999997e-35

   1. Initial program 95.3%

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

   2. Taylor expanded in b around inf 83.8%

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

      1. mul-1-neg 83.8%

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

      2. distribute-rgt-neg-out 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in a around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. unsub-neg 45.4%

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

      3. *-commutative 45.4%

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

   7. Simplified 45.4%

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

   if 5.4999999999999997e-35 < y

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. distribute-lft-neg-out 67.6%

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

      3. *-commutative 67.6%

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

   4. Simplified 67.6%

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

   5. Taylor expanded in y around 0 26.4%

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

      1. mul-1-neg 26.4%

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

      2. unsub-neg 26.4%

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

      3. *-commutative 26.4%

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

   7. Simplified 26.4%

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

   8. Taylor expanded in y around inf 26.7%

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

      1. mul-1-neg 26.7%

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

      2. associate-*r* 36.7%

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

      3. distribute-lft-neg-in 36.7%

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

      4. *-commutative 36.7%

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

   10. Simplified 36.7%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-35}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 16: 29.6% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-253}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-35}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.6e-253)
   (- x (* t (* x y)))
   (if (<= y 1.06e-35) (- x (* a (* x b))) (* y (* x (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.6e-253) {
		tmp = x - (t * (x * y));
	} else if (y <= 1.06e-35) {
		tmp = x - (a * (x * b));
	} else {
		tmp = y * (x * -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 (y <= (-3.6d-253)) then
        tmp = x - (t * (x * y))
    else if (y <= 1.06d-35) then
        tmp = x - (a * (x * b))
    else
        tmp = y * (x * -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 (y <= -3.6e-253) {
		tmp = x - (t * (x * y));
	} else if (y <= 1.06e-35) {
		tmp = x - (a * (x * b));
	} else {
		tmp = y * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.6e-253:
		tmp = x - (t * (x * y))
	elif y <= 1.06e-35:
		tmp = x - (a * (x * b))
	else:
		tmp = y * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.6e-253)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (y <= 1.06e-35)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	else
		tmp = Float64(y * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.6e-253)
		tmp = x - (t * (x * y));
	elseif (y <= 1.06e-35)
		tmp = x - (a * (x * b));
	else
		tmp = y * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.6e-253], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e-35], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e-253

   1. Initial program 95.8%

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

   2. Taylor expanded in t around inf 63.8%

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

      1. mul-1-neg 63.8%

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

      2. distribute-lft-neg-out 63.8%

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

      3. *-commutative 63.8%

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

   4. Simplified 63.8%

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

   5. Taylor expanded in y around 0 31.1%

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

      1. mul-1-neg 31.1%

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

      2. unsub-neg 31.1%

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

      3. *-commutative 31.1%

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

   7. Simplified 31.1%

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

   if -3.6e-253 < y < 1.06e-35

   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 b around inf 91.5%

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

      1. mul-1-neg 91.5%

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

      2. distribute-rgt-neg-out 91.5%

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

   4. Simplified 91.5%

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

   5. Taylor expanded in a around 0 49.8%

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

      1. mul-1-neg 49.8%

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

      2. unsub-neg 49.8%

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

      3. *-commutative 49.8%

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

   7. Simplified 49.8%

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

   if 1.06e-35 < y

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. distribute-lft-neg-out 67.6%

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

      3. *-commutative 67.6%

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

   4. Simplified 67.6%

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

   5. Taylor expanded in y around 0 26.4%

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

      1. mul-1-neg 26.4%

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

      2. unsub-neg 26.4%

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

      3. *-commutative 26.4%

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

   7. Simplified 26.4%

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

   8. Taylor expanded in y around inf 26.7%

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

      1. mul-1-neg 26.7%

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

      2. associate-*r* 36.7%

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

      3. distribute-lft-neg-in 36.7%

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

      4. *-commutative 36.7%

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

   10. Simplified 36.7%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-253}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-35}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 17: 25.3% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+90} \lor \neg \left(y \leq 1.9 \cdot 10^{-74}\right):\\ \;\;\;\;-b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7e+90) (not (<= y 1.9e-74))) (- (* b (* x a))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7e+90) || !(y <= 1.9e-74)) {
		tmp = -(b * (x * a));
	} 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 <= (-7d+90)) .or. (.not. (y <= 1.9d-74))) then
        tmp = -(b * (x * a))
    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 <= -7e+90) || !(y <= 1.9e-74)) {
		tmp = -(b * (x * a));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7e+90) or not (y <= 1.9e-74):
		tmp = -(b * (x * a))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7e+90) || !(y <= 1.9e-74))
		tmp = Float64(-Float64(b * Float64(x * a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7e+90) || ~((y <= 1.9e-74)))
		tmp = -(b * (x * a));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7e+90], N[Not[LessEqual[y, 1.9e-74]], $MachinePrecision]], (-N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), x]

Derivation

1. Split input into 2 regimes

2. if y < -6.9999999999999997e90 or 1.8999999999999998e-74 < y

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 49.8%

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

      1. sub-neg 49.8%

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

      2. neg-mul-1 49.8%

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

      3. log1p-def 50.6%

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

      4. neg-mul-1 50.6%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in z around 0 50.6%

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

      1. associate-*r* 50.6%

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

      2. associate-*r* 50.6%

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

      3. distribute-lft-out 50.6%

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

      4. mul-1-neg 50.6%

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

      5. +-commutative 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in a around 0 18.7%

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

      1. mul-1-neg 18.7%

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

      2. unsub-neg 18.7%

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

      3. *-commutative 18.7%

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

      4. associate-*l* 18.7%

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

      5. *-commutative 18.7%

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

   10. Simplified 18.7%

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

   11. Taylor expanded in b around inf 22.7%

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

       1. mul-1-neg 22.7%

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

       2. *-commutative 22.7%

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

       3. associate-*r* 21.2%

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

       4. *-commutative 21.2%

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

   13. Simplified 21.2%

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

   if -6.9999999999999997e90 < y < 1.8999999999999998e-74

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf 65.9%

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

   3. Taylor expanded in y around 0 36.9%

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

4. Final simplification 28.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+90} \lor \neg \left(y \leq 1.9 \cdot 10^{-74}\right):\\ \;\;\;\;-b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 27.0% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-9} \lor \neg \left(y \leq 4.5 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.2e-9) (not (<= y 4.5e-35))) (* x (* y (- t))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.2e-9) || !(y <= 4.5e-35)) {
		tmp = x * (y * -t);
	} 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 <= (-4.2d-9)) .or. (.not. (y <= 4.5d-35))) then
        tmp = x * (y * -t)
    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 <= -4.2e-9) || !(y <= 4.5e-35)) {
		tmp = x * (y * -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.2e-9) or not (y <= 4.5e-35):
		tmp = x * (y * -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.2e-9) || !(y <= 4.5e-35))
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.2e-9) || ~((y <= 4.5e-35)))
		tmp = x * (y * -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.2e-9], N[Not[LessEqual[y, 4.5e-35]], $MachinePrecision]], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000039e-9 or 4.5000000000000001e-35 < y

   1. Initial program 96.2%

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

   2. Taylor expanded in t around inf 64.0%

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

      1. mul-1-neg 64.0%

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

      2. distribute-lft-neg-out 64.0%

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

      3. *-commutative 64.0%

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

   4. Simplified 64.0%

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

   5. Taylor expanded in y around 0 23.5%

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

      1. mul-1-neg 23.5%

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

      2. unsub-neg 23.5%

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

      3. *-commutative 23.5%

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

   7. Simplified 23.5%

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

   8. Taylor expanded in y around inf 26.3%

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

      1. mul-1-neg 26.3%

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

      2. distribute-rgt-neg-in 26.3%

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

   10. Simplified 26.3%

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

   if -4.20000000000000039e-9 < y < 4.5000000000000001e-35

   1. Initial program 95.2%

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

   2. Taylor expanded in y around inf 61.0%

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

   3. Taylor expanded in y around 0 40.4%

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

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-9} \lor \neg \left(y \leq 4.5 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 26.9% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-8} \lor \neg \left(y \leq 5.5 \cdot 10^{-35}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.2e-8) (not (<= y 5.5e-35))) (* y (* x (- t))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.2e-8) || !(y <= 5.5e-35)) {
		tmp = y * (x * -t);
	} 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 <= (-8.2d-8)) .or. (.not. (y <= 5.5d-35))) then
        tmp = y * (x * -t)
    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 <= -8.2e-8) || !(y <= 5.5e-35)) {
		tmp = y * (x * -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.2e-8) or not (y <= 5.5e-35):
		tmp = y * (x * -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.2e-8) || !(y <= 5.5e-35))
		tmp = Float64(y * Float64(x * Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.2e-8) || ~((y <= 5.5e-35)))
		tmp = y * (x * -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.2e-8], N[Not[LessEqual[y, 5.5e-35]], $MachinePrecision]], N[(y * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.20000000000000063e-8 or 5.4999999999999997e-35 < y

   1. Initial program 96.2%

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

   2. Taylor expanded in t around inf 64.0%

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

      1. mul-1-neg 64.0%

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

      2. distribute-lft-neg-out 64.0%

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

      3. *-commutative 64.0%

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

   4. Simplified 64.0%

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

   5. Taylor expanded in y around 0 23.5%

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

      1. mul-1-neg 23.5%

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

      2. unsub-neg 23.5%

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

      3. *-commutative 23.5%

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

   7. Simplified 23.5%

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

   8. Taylor expanded in y around inf 24.9%

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

      1. mul-1-neg 24.9%

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

      2. associate-*r* 29.2%

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

      3. distribute-lft-neg-in 29.2%

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

      4. *-commutative 29.2%

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

   10. Simplified 29.2%

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

   if -8.20000000000000063e-8 < y < 5.4999999999999997e-35

   1. Initial program 95.2%

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

   2. Taylor expanded in y around inf 61.0%

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

   3. Taylor expanded in y around 0 40.4%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-8} \lor \neg \left(y \leq 5.5 \cdot 10^{-35}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 25.7% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-b \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.85e-40)
   (* a (* x (- z)))
   (if (<= y 2.5e-74) x (- (* b (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.85e-40) {
		tmp = a * (x * -z);
	} else if (y <= 2.5e-74) {
		tmp = x;
	} else {
		tmp = -(b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.85d-40)) then
        tmp = a * (x * -z)
    else if (y <= 2.5d-74) then
        tmp = x
    else
        tmp = -(b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.85e-40) {
		tmp = a * (x * -z);
	} else if (y <= 2.5e-74) {
		tmp = x;
	} else {
		tmp = -(b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.85e-40:
		tmp = a * (x * -z)
	elif y <= 2.5e-74:
		tmp = x
	else:
		tmp = -(b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.85e-40)
		tmp = Float64(a * Float64(x * Float64(-z)));
	elseif (y <= 2.5e-74)
		tmp = x;
	else
		tmp = Float64(-Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.85e-40)
		tmp = a * (x * -z);
	elseif (y <= 2.5e-74)
		tmp = x;
	else
		tmp = -(b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.85e-40], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-74], x, (-N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if y < -2.84999999999999992e-40

   1. Initial program 97.2%

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

   2. Taylor expanded in y around 0 45.1%

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

      1. sub-neg 45.1%

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

      2. neg-mul-1 45.1%

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

      3. log1p-def 45.0%

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

      4. neg-mul-1 45.0%

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

   4. Simplified 45.0%

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

   5. Taylor expanded in z around 0 45.0%

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

      1. associate-*r* 45.0%

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

      2. associate-*r* 45.0%

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

      3. distribute-lft-out 45.0%

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

      4. mul-1-neg 45.0%

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

      5. +-commutative 45.0%

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

   7. Simplified 45.0%

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

   8. Taylor expanded in a around 0 13.1%

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

      1. mul-1-neg 13.1%

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

      2. unsub-neg 13.1%

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

      3. *-commutative 13.1%

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

      4. associate-*l* 13.1%

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

      5. *-commutative 13.1%

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

   10. Simplified 13.1%

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

   11. Taylor expanded in z around inf 15.4%

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

       1. mul-1-neg 15.4%

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

       2. distribute-rgt-neg-in 15.4%

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

   13. Simplified 15.4%

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

   if -2.84999999999999992e-40 < y < 2.49999999999999999e-74

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 59.8%

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

   3. Taylor expanded in y around 0 43.4%

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

   if 2.49999999999999999e-74 < y

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 52.9%

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

      1. sub-neg 52.9%

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

      2. neg-mul-1 52.9%

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

      3. log1p-def 54.1%

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

      4. neg-mul-1 54.1%

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

   4. Simplified 54.1%

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

   5. Taylor expanded in z around 0 54.1%

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

      1. associate-*r* 54.1%

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

      2. associate-*r* 54.1%

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

      3. distribute-lft-out 54.1%

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

      4. mul-1-neg 54.1%

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

      5. +-commutative 54.1%

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

   7. Simplified 54.1%

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

   8. Taylor expanded in a around 0 21.0%

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

      1. mul-1-neg 21.0%

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

      2. unsub-neg 21.0%

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

      3. *-commutative 21.0%

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

      4. associate-*l* 22.2%

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

      5. *-commutative 22.2%

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

   10. Simplified 22.2%

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

   11. Taylor expanded in b around inf 26.9%

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

       1. mul-1-neg 26.9%

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

       2. *-commutative 26.9%

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

       3. associate-*r* 25.6%

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

       4. *-commutative 25.6%

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

   13. Simplified 25.6%

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

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-b \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 21: 21.1% accurate, 34.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+168} \lor \neg \left(a \leq 1.6 \cdot 10^{+97}\right):\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.6e+168) (not (<= a 1.6e+97))) (* x (* y t)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.6e+168) || !(a <= 1.6e+97)) {
		tmp = x * (y * t);
	} 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 ((a <= (-1.6d+168)) .or. (.not. (a <= 1.6d+97))) then
        tmp = x * (y * t)
    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 ((a <= -1.6e+168) || !(a <= 1.6e+97)) {
		tmp = x * (y * t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.6e+168) or not (a <= 1.6e+97):
		tmp = x * (y * t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.6e+168) || !(a <= 1.6e+97))
		tmp = Float64(x * Float64(y * t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.6e+168) || ~((a <= 1.6e+97)))
		tmp = x * (y * t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.6e+168], N[Not[LessEqual[a, 1.6e+97]], $MachinePrecision]], N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.6000000000000001e168 or 1.60000000000000008e97 < a

   1. Initial program 86.0%

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

   2. Taylor expanded in t around inf 42.1%

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

      1. mul-1-neg 42.1%

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

      2. distribute-lft-neg-out 42.1%

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

      3. *-commutative 42.1%

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

   4. Simplified 42.1%

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

   5. Taylor expanded in y around 0 11.5%

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

      1. mul-1-neg 11.5%

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

      2. unsub-neg 11.5%

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

      3. *-commutative 11.5%

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

   7. Simplified 11.5%

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

   8. Taylor expanded in y around inf 27.3%

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

      1. mul-1-neg 27.3%

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

      2. distribute-rgt-neg-in 27.3%

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

   10. Simplified 27.3%

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

       1. expm1-log1p-u 22.6%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(t \cdot \left(-y\right)\right)\right)\right)} \]

       2. expm1-udef 29.4%

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

       3. *-commutative 29.4%

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

       4. add-sqr-sqrt 10.5%

          \[\leadsto e^{\mathsf{log1p}\left(x \cdot \left(\color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \cdot t\right)\right)} - 1 \]

       5. sqrt-unprod 33.8%

          \[\leadsto e^{\mathsf{log1p}\left(x \cdot \left(\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \cdot t\right)\right)} - 1 \]

       6. sqr-neg 33.8%

          \[\leadsto e^{\mathsf{log1p}\left(x \cdot \left(\sqrt{\color{blue}{y \cdot y}} \cdot t\right)\right)} - 1 \]

       7. sqrt-unprod 17.7%

          \[\leadsto e^{\mathsf{log1p}\left(x \cdot \left(\color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot t\right)\right)} - 1 \]

       8. add-sqr-sqrt 26.5%

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

   12. Applied egg-rr 26.5%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(x \cdot \left(y \cdot t\right)\right)} - 1} \]
   13. Step-by-step derivation

       1. expm1-def 19.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot t\right)\right)\right)} \]

       2. expm1-log1p 21.9%

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

   14. Simplified 21.9%

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

   if -1.6000000000000001e168 < a < 1.60000000000000008e97

   1. Initial program 99.4%

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

   2. Taylor expanded in y around inf 84.8%

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

   3. Taylor expanded in y around 0 28.1%

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

4. Final simplification 26.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+168} \lor \neg \left(a \leq 1.6 \cdot 10^{+97}\right):\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 18.9% 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 95.8%

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

2. Taylor expanded in y around inf 75.4%

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

3. Taylor expanded in y around 0 21.9%

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

4. Final simplification 21.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023297 
(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))))))