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

Percentage Accurate: 96.6% → 99.5%

Time: 23.1s

Alternatives: 19

Speedup: 1.0×

• 20.2% 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: 96.6% 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: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. fma-def 96.9%

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

   2. sub-neg 96.9%

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

   3. log1p-def 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

2. Final simplification 96.5%

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

Alternative 3: 86.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-23} \lor \neg \left(y \leq 3 \cdot 10^{-110}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{z \cdot \left(-a\right) - a \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.02e-23) (not (<= y 3e-110)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (- (* z (- a)) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.02e-23) || !(y <= 3e-110)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp(((z * -a) - (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 <= (-1.02d-23)) .or. (.not. (y <= 3d-110))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp(((z * -a) - (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 <= -1.02e-23) || !(y <= 3e-110)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp(((z * -a) - (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.02e-23) or not (y <= 3e-110):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp(((z * -a) - (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.02e-23) || !(y <= 3e-110))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(Float64(z * Float64(-a)) - Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.02e-23) || ~((y <= 3e-110)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp(((z * -a) - (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.02e-23], N[Not[LessEqual[y, 3e-110]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(N[(z * (-a)), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02000000000000005e-23 or 2.99999999999999986e-110 < y

   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 87.5%

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

   if -1.02000000000000005e-23 < y < 2.99999999999999986e-110

   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 86.5%

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

      1. sub-neg 86.5%

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

      2. sub-neg 86.5%

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

      3. neg-mul-1 86.5%

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

      4. log1p-def 92.0%

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

      5. neg-mul-1 92.0%

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

      6. sub-neg 92.0%

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

   4. Simplified 92.0%

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

   5. Taylor expanded in z around 0 92.0%

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

      1. mul-1-neg 92.0%

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

      2. unsub-neg 92.0%

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

      3. mul-1-neg 92.0%

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

      4. distribute-rgt-neg-in 92.0%

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

   7. Simplified 92.0%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-23} \lor \neg \left(y \leq 3 \cdot 10^{-110}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{z \cdot \left(-a\right) - a \cdot b}\\ \end{array} \]

Alternative 4: 75.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+129} \lor \neg \left(y \leq 7.2 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{z \cdot \left(-a\right) - a \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.6e+129) (not (<= y 7.2e-7)))
   (* x (pow z y))
   (* x (exp (- (* z (- a)) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.6e+129) || !(y <= 7.2e-7)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp(((z * -a) - (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+129)) .or. (.not. (y <= 7.2d-7))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp(((z * -a) - (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+129) || !(y <= 7.2e-7)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp(((z * -a) - (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.6e+129) or not (y <= 7.2e-7):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp(((z * -a) - (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.6e+129) || !(y <= 7.2e-7))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(Float64(z * Float64(-a)) - Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.6e+129) || ~((y <= 7.2e-7)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp(((z * -a) - (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.6e+129], N[Not[LessEqual[y, 7.2e-7]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(N[(z * (-a)), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6000000000000001e129 or 7.19999999999999989e-7 < y

   1. Initial program 98.1%

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

   2. Taylor expanded in y around inf 92.6%

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

   3. Taylor expanded in t around 0 74.9%

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

   if -1.6000000000000001e129 < y < 7.19999999999999989e-7

   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 77.6%

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

      1. sub-neg 77.6%

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

      2. sub-neg 77.6%

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

      3. neg-mul-1 77.6%

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

      4. log1p-def 83.4%

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

      5. neg-mul-1 83.4%

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

      6. sub-neg 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in z around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. unsub-neg 83.4%

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

      3. mul-1-neg 83.4%

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

      4. distribute-rgt-neg-in 83.4%

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

   7. Simplified 83.4%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+129} \lor \neg \left(y \leq 7.2 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{z \cdot \left(-a\right) - a \cdot b}\\ \end{array} \]

Alternative 5: 74.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+33} \lor \neg \left(y \leq 5.5 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.4e+33) (not (<= y 5.5e-7)))
   (* 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 <= -2.4e+33) || !(y <= 5.5e-7)) {
		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 <= (-2.4d+33)) .or. (.not. (y <= 5.5d-7))) 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 <= -2.4e+33) || !(y <= 5.5e-7)) {
		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 <= -2.4e+33) or not (y <= 5.5e-7):
		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 <= -2.4e+33) || !(y <= 5.5e-7))
		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 <= -2.4e+33) || ~((y <= 5.5e-7)))
		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, -2.4e+33], N[Not[LessEqual[y, 5.5e-7]], $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 < -2.4e33 or 5.5000000000000003e-7 < y

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 89.7%

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

   3. Taylor expanded in t around 0 71.4%

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

   if -2.4e33 < y < 5.5000000000000003e-7

   1. Initial program 95.6%

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

   2. Taylor expanded in b around inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. distribute-rgt-neg-out 80.3%

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

   4. Simplified 80.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+33} \lor \neg \left(y \leq 5.5 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 6: 72.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.5e-27)
   (* x (exp (* y (- t))))
   (if (<= y 7.2e-7) (* x (exp (* a (- b)))) (* x (pow z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.5e-27) {
		tmp = x * exp((y * -t));
	} else if (y <= 7.2e-7) {
		tmp = x * exp((a * -b));
	} 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 (y <= (-4.5d-27)) then
        tmp = x * exp((y * -t))
    else if (y <= 7.2d-7) then
        tmp = x * exp((a * -b))
    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 (y <= -4.5e-27) {
		tmp = x * Math.exp((y * -t));
	} else if (y <= 7.2e-7) {
		tmp = x * Math.exp((a * -b));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.5e-27:
		tmp = x * math.exp((y * -t))
	elif y <= 7.2e-7:
		tmp = x * math.exp((a * -b))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.5e-27)
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	elseif (y <= 7.2e-7)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	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 (y <= -4.5e-27)
		tmp = x * exp((y * -t));
	elseif (y <= 7.2e-7)
		tmp = x * exp((a * -b));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.5e-27], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-7], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5000000000000002e-27

   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 66.3%

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

      1. mul-1-neg 66.3%

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

      2. distribute-lft-neg-out 66.3%

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

      3. *-commutative 66.3%

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

   4. Simplified 66.3%

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

   if -4.5000000000000002e-27 < y < 7.19999999999999989e-7

   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 b around inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-rgt-neg-out 82.5%

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

   4. Simplified 82.5%

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

   if 7.19999999999999989e-7 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in y around inf 90.0%

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

   3. Taylor expanded in t around 0 74.3%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 7: 56.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.72 \lor \neg \left(y \leq 3.7 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.72) (not (<= y 3.7e-10)))
   (* x (pow z y))
   (- x (* b (* x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.72) || !(y <= 3.7e-10)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x - (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 <= (-0.72d0)) .or. (.not. (y <= 3.7d-10))) then
        tmp = x * (z ** y)
    else
        tmp = x - (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 <= -0.72) || !(y <= 3.7e-10)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x - (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -0.72) or not (y <= 3.7e-10):
		tmp = x * math.pow(z, y)
	else:
		tmp = x - (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -0.72) || !(y <= 3.7e-10))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x - 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 <= -0.72) || ~((y <= 3.7e-10)))
		tmp = x * (z ^ y);
	else
		tmp = x - (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -0.72], N[Not[LessEqual[y, 3.7e-10]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.71999999999999997 or 3.70000000000000015e-10 < y

   1. Initial program 97.7%

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

   2. Taylor expanded in y around inf 90.0%

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

   3. Taylor expanded in t around 0 70.8%

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

   if -0.71999999999999997 < y < 3.70000000000000015e-10

   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 80.5%

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

      1. mul-1-neg 80.5%

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

      2. distribute-rgt-neg-out 80.5%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in a around 0 42.5%

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

      1. mul-1-neg 42.5%

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

      2. unsub-neg 42.5%

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

   7. Simplified 42.5%

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

      1. cancel-sign-sub-inv 42.5%

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

      2. *-commutative 42.5%

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

      3. associate-*r* 48.5%

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

   9. Applied egg-rr 48.5%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.72 \lor \neg \left(y \leq 3.7 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 8: 26.5% accurate, 16.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-z\right)\right)\\ t_2 := x \cdot \left(1 - y \cdot t\right)\\ \mathbf{if}\;a \leq -1.32 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.0175:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+158}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+201}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* x (- z)))) (t_2 (* x (- 1.0 (* y t)))))
   (if (<= a -1.32e+141)
     t_1
     (if (<= a -4.8e-80)
       (* x (* y (- t)))
       (if (<= a -2.05e-175)
         t_1
         (if (<= a 0.0175)
           t_2
           (if (<= a 2e+158)
             (* a (* x (- b)))
             (if (<= a 4e+201) t_2 (* x (* y t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (x * -z);
	double t_2 = x * (1.0 - (y * t));
	double tmp;
	if (a <= -1.32e+141) {
		tmp = t_1;
	} else if (a <= -4.8e-80) {
		tmp = x * (y * -t);
	} else if (a <= -2.05e-175) {
		tmp = t_1;
	} else if (a <= 0.0175) {
		tmp = t_2;
	} else if (a <= 2e+158) {
		tmp = a * (x * -b);
	} else if (a <= 4e+201) {
		tmp = t_2;
	} else {
		tmp = x * (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (x * -z)
    t_2 = x * (1.0d0 - (y * t))
    if (a <= (-1.32d+141)) then
        tmp = t_1
    else if (a <= (-4.8d-80)) then
        tmp = x * (y * -t)
    else if (a <= (-2.05d-175)) then
        tmp = t_1
    else if (a <= 0.0175d0) then
        tmp = t_2
    else if (a <= 2d+158) then
        tmp = a * (x * -b)
    else if (a <= 4d+201) then
        tmp = t_2
    else
        tmp = x * (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 t_1 = a * (x * -z);
	double t_2 = x * (1.0 - (y * t));
	double tmp;
	if (a <= -1.32e+141) {
		tmp = t_1;
	} else if (a <= -4.8e-80) {
		tmp = x * (y * -t);
	} else if (a <= -2.05e-175) {
		tmp = t_1;
	} else if (a <= 0.0175) {
		tmp = t_2;
	} else if (a <= 2e+158) {
		tmp = a * (x * -b);
	} else if (a <= 4e+201) {
		tmp = t_2;
	} else {
		tmp = x * (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (x * -z)
	t_2 = x * (1.0 - (y * t))
	tmp = 0
	if a <= -1.32e+141:
		tmp = t_1
	elif a <= -4.8e-80:
		tmp = x * (y * -t)
	elif a <= -2.05e-175:
		tmp = t_1
	elif a <= 0.0175:
		tmp = t_2
	elif a <= 2e+158:
		tmp = a * (x * -b)
	elif a <= 4e+201:
		tmp = t_2
	else:
		tmp = x * (y * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(x * Float64(-z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y * t)))
	tmp = 0.0
	if (a <= -1.32e+141)
		tmp = t_1;
	elseif (a <= -4.8e-80)
		tmp = Float64(x * Float64(y * Float64(-t)));
	elseif (a <= -2.05e-175)
		tmp = t_1;
	elseif (a <= 0.0175)
		tmp = t_2;
	elseif (a <= 2e+158)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (a <= 4e+201)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (x * -z);
	t_2 = x * (1.0 - (y * t));
	tmp = 0.0;
	if (a <= -1.32e+141)
		tmp = t_1;
	elseif (a <= -4.8e-80)
		tmp = x * (y * -t);
	elseif (a <= -2.05e-175)
		tmp = t_1;
	elseif (a <= 0.0175)
		tmp = t_2;
	elseif (a <= 2e+158)
		tmp = a * (x * -b);
	elseif (a <= 4e+201)
		tmp = t_2;
	else
		tmp = x * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.32e+141], t$95$1, If[LessEqual[a, -4.8e-80], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.05e-175], t$95$1, If[LessEqual[a, 0.0175], t$95$2, If[LessEqual[a, 2e+158], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+201], t$95$2, N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.3200000000000001e141 or -4.7999999999999998e-80 < a < -2.04999999999999999e-175

   1. Initial program 92.7%

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

   2. Taylor expanded in y around 0 54.7%

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

      1. sub-neg 54.7%

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

      2. sub-neg 54.7%

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

      3. neg-mul-1 54.7%

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

      4. log1p-def 63.9%

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

      5. neg-mul-1 63.9%

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

      6. sub-neg 63.9%

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

   4. Simplified 63.9%

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

   5. Taylor expanded in b around 0 10.3%

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

   6. Taylor expanded in z around 0 15.8%

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

      1. neg-mul-1 15.8%

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

      2. distribute-rgt-neg-in 15.8%

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

   8. Simplified 15.8%

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

   9. Taylor expanded in a around inf 31.4%

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

       1. associate-*r* 31.4%

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

       2. neg-mul-1 31.4%

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

   11. Simplified 31.4%

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

   if -1.3200000000000001e141 < a < -4.7999999999999998e-80

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf 42.9%

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

      1. mul-1-neg 42.9%

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

      2. distribute-lft-neg-out 42.9%

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

      3. *-commutative 42.9%

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

   4. Simplified 42.9%

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

   5. Taylor expanded in y around 0 19.4%

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

      1. mul-1-neg 19.4%

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

      2. unsub-neg 19.4%

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

      3. *-commutative 19.4%

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

   7. Simplified 19.4%

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

   8. Taylor expanded in y around inf 24.2%

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

      1. associate-*r* 24.2%

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

      2. neg-mul-1 24.2%

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

      3. *-commutative 24.2%

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

   10. Simplified 24.2%

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

   if -2.04999999999999999e-175 < a < 0.017500000000000002 or 1.99999999999999991e158 < a < 4.00000000000000015e201

   1. Initial program 99.0%

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

   2. Taylor expanded in t around inf 75.6%

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

      1. mul-1-neg 75.6%

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

      2. distribute-lft-neg-out 75.6%

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

      3. *-commutative 75.6%

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

   4. Simplified 75.6%

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

   5. Taylor expanded in y around 0 49.8%

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

      1. mul-1-neg 49.8%

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

      2. unsub-neg 49.8%

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

      3. *-commutative 49.8%

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

   7. Simplified 49.8%

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

   if 0.017500000000000002 < a < 1.99999999999999991e158

   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 b around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. distribute-rgt-neg-out 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in a around 0 24.2%

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

      1. mul-1-neg 24.2%

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

      2. unsub-neg 24.2%

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

   7. Simplified 24.2%

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

   8. Taylor expanded in a around inf 24.0%

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

   if 4.00000000000000015e201 < a

   1. Initial program 90.1%

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

   2. Taylor expanded in t around inf 32.7%

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

      1. mul-1-neg 32.7%

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

      2. distribute-lft-neg-out 32.7%

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

      3. *-commutative 32.7%

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

   4. Simplified 32.7%

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

   5. Taylor expanded in y around 0 3.6%

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

      1. mul-1-neg 3.6%

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

      2. unsub-neg 3.6%

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

      3. *-commutative 3.6%

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

   7. Simplified 3.6%

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

   8. Taylor expanded in y around inf 41.6%

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

      1. associate-*r* 41.6%

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

      2. neg-mul-1 41.6%

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

      3. *-commutative 41.6%

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

   10. Simplified 41.6%

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

       1. expm1-log1p-u 40.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot \left(-t\right)\right)\right)\right)} \]

       2. expm1-udef 50.5%

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

       3. *-commutative 50.5%

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

       4. *-commutative 50.5%

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

       5. associate-*l* 50.5%

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

       6. add-sqr-sqrt 30.2%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)} \cdot \left(y \cdot x\right)\right)} - 1 \]

       7. sqrt-unprod 50.2%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}} \cdot \left(y \cdot x\right)\right)} - 1 \]

       8. sqr-neg 50.2%

          \[\leadsto e^{\mathsf{log1p}\left(\sqrt{\color{blue}{t \cdot t}} \cdot \left(y \cdot x\right)\right)} - 1 \]

       9. sqrt-unprod 20.7%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)} \cdot \left(y \cdot x\right)\right)} - 1 \]

       10. add-sqr-sqrt 51.1%

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

   12. Applied egg-rr 51.1%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(t \cdot \left(y \cdot x\right)\right)} - 1} \]
   13. Step-by-step derivation

       1. expm1-def 32.4%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot x\right)\right)\right)} \]

       2. expm1-log1p 32.5%

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

       3. associate-*r* 46.3%

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

       4. *-commutative 46.3%

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

   14. Simplified 46.3%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+141}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-175}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 0.0175:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+158}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+201}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 9: 32.4% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-64}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.5:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t) (* x y))))
   (if (<= y -3e+88)
     t_1
     (if (<= y -4.5e-64)
       (* a (* x (- b)))
       (if (<= y -3.5e-75)
         t_1
         (if (<= y 0.5) (- x (* b (* x a))) (* x (* a (- b)))))))))

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 <= -3e+88) {
		tmp = t_1;
	} else if (y <= -4.5e-64) {
		tmp = a * (x * -b);
	} else if (y <= -3.5e-75) {
		tmp = t_1;
	} else if (y <= 0.5) {
		tmp = x - (b * (x * a));
	} else {
		tmp = x * (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) :: t_1
    real(8) :: tmp
    t_1 = -t * (x * y)
    if (y <= (-3d+88)) then
        tmp = t_1
    else if (y <= (-4.5d-64)) then
        tmp = a * (x * -b)
    else if (y <= (-3.5d-75)) then
        tmp = t_1
    else if (y <= 0.5d0) then
        tmp = x - (b * (x * a))
    else
        tmp = x * (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 t_1 = -t * (x * y);
	double tmp;
	if (y <= -3e+88) {
		tmp = t_1;
	} else if (y <= -4.5e-64) {
		tmp = a * (x * -b);
	} else if (y <= -3.5e-75) {
		tmp = t_1;
	} else if (y <= 0.5) {
		tmp = x - (b * (x * a));
	} else {
		tmp = x * (a * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -t * (x * y)
	tmp = 0
	if y <= -3e+88:
		tmp = t_1
	elif y <= -4.5e-64:
		tmp = a * (x * -b)
	elif y <= -3.5e-75:
		tmp = t_1
	elif y <= 0.5:
		tmp = x - (b * (x * a))
	else:
		tmp = x * (a * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-t) * Float64(x * y))
	tmp = 0.0
	if (y <= -3e+88)
		tmp = t_1;
	elseif (y <= -4.5e-64)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= -3.5e-75)
		tmp = t_1;
	elseif (y <= 0.5)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	else
		tmp = Float64(x * Float64(a * Float64(-b)));
	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 <= -3e+88)
		tmp = t_1;
	elseif (y <= -4.5e-64)
		tmp = a * (x * -b);
	elseif (y <= -3.5e-75)
		tmp = t_1;
	elseif (y <= 0.5)
		tmp = x - (b * (x * a));
	else
		tmp = x * (a * -b);
	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, -3e+88], t$95$1, If[LessEqual[y, -4.5e-64], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-75], t$95$1, If[LessEqual[y, 0.5], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.00000000000000005e88 or -4.5000000000000001e-64 < y < -3.49999999999999985e-75

   1. Initial program 97.9%

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

   2. Taylor expanded in t around inf 68.8%

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

      1. mul-1-neg 68.8%

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

      2. distribute-lft-neg-out 68.8%

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

      3. *-commutative 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in y around 0 21.5%

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

      1. mul-1-neg 21.5%

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

      2. unsub-neg 21.5%

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

      3. *-commutative 21.5%

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

   7. Simplified 21.5%

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

   8. Taylor expanded in y around inf 27.5%

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

      1. associate-*r* 27.5%

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

      2. neg-mul-1 27.5%

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

   10. Simplified 27.5%

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

   if -3.00000000000000005e88 < y < -4.5000000000000001e-64

   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 52.6%

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

      1. mul-1-neg 52.6%

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

      2. distribute-rgt-neg-out 52.6%

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

   4. Simplified 52.6%

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

   5. Taylor expanded in a around 0 20.1%

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

      1. mul-1-neg 20.1%

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

      2. unsub-neg 20.1%

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

   7. Simplified 20.1%

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

   8. Taylor expanded in a around inf 27.0%

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

   if -3.49999999999999985e-75 < y < 0.5

   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 b around inf 81.1%

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

      1. mul-1-neg 81.1%

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

      2. distribute-rgt-neg-out 81.1%

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

   4. Simplified 81.1%

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

   5. Taylor expanded in a around 0 44.3%

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

      1. mul-1-neg 44.3%

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

      2. unsub-neg 44.3%

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

   7. Simplified 44.3%

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

      1. cancel-sign-sub-inv 44.3%

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

      2. *-commutative 44.3%

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

      3. associate-*r* 50.8%

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

   9. Applied egg-rr 50.8%

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

   if 0.5 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in b around inf 38.2%

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

      1. mul-1-neg 38.2%

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

      2. distribute-rgt-neg-out 38.2%

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

   4. Simplified 38.2%

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

   5. Taylor expanded in a around 0 12.1%

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

      1. mul-1-neg 12.1%

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

      2. unsub-neg 12.1%

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

   7. Simplified 12.1%

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

   8. Taylor expanded in a around inf 25.9%

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

      1. mul-1-neg 25.9%

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

      2. associate-*r* 26.9%

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

      3. distribute-lft-neg-in 26.9%

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

      4. mul-1-neg 26.9%

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

      5. *-commutative 26.9%

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

      6. associate-*r* 26.9%

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

      7. neg-mul-1 26.9%

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

   10. Simplified 26.9%

       \[\leadsto \color{blue}{x \cdot \left(\left(-a\right) \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+88}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-64}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 0.5:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 10: 28.9% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-101}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* a (- b)))))
   (if (<= y -2.1e+85)
     (* x (* y (- t)))
     (if (<= y -1.5e-22)
       t_1
       (if (<= y -1.8e-101) (* a (* x (- z))) (if (<= y 1.05e-10) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (a * -b);
	double tmp;
	if (y <= -2.1e+85) {
		tmp = x * (y * -t);
	} else if (y <= -1.5e-22) {
		tmp = t_1;
	} else if (y <= -1.8e-101) {
		tmp = a * (x * -z);
	} else if (y <= 1.05e-10) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (a * -b)
    if (y <= (-2.1d+85)) then
        tmp = x * (y * -t)
    else if (y <= (-1.5d-22)) then
        tmp = t_1
    else if (y <= (-1.8d-101)) then
        tmp = a * (x * -z)
    else if (y <= 1.05d-10) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (a * -b);
	double tmp;
	if (y <= -2.1e+85) {
		tmp = x * (y * -t);
	} else if (y <= -1.5e-22) {
		tmp = t_1;
	} else if (y <= -1.8e-101) {
		tmp = a * (x * -z);
	} else if (y <= 1.05e-10) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (a * -b)
	tmp = 0
	if y <= -2.1e+85:
		tmp = x * (y * -t)
	elif y <= -1.5e-22:
		tmp = t_1
	elif y <= -1.8e-101:
		tmp = a * (x * -z)
	elif y <= 1.05e-10:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(a * Float64(-b)))
	tmp = 0.0
	if (y <= -2.1e+85)
		tmp = Float64(x * Float64(y * Float64(-t)));
	elseif (y <= -1.5e-22)
		tmp = t_1;
	elseif (y <= -1.8e-101)
		tmp = Float64(a * Float64(x * Float64(-z)));
	elseif (y <= 1.05e-10)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (a * -b);
	tmp = 0.0;
	if (y <= -2.1e+85)
		tmp = x * (y * -t);
	elseif (y <= -1.5e-22)
		tmp = t_1;
	elseif (y <= -1.8e-101)
		tmp = a * (x * -z);
	elseif (y <= 1.05e-10)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+85], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.5e-22], t$95$1, If[LessEqual[y, -1.8e-101], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-10], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.1000000000000001e85

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. distribute-lft-neg-out 71.1%

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

      3. *-commutative 71.1%

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

   4. Simplified 71.1%

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

   5. Taylor expanded in y around 0 20.4%

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

      1. mul-1-neg 20.4%

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

      2. unsub-neg 20.4%

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

      3. *-commutative 20.4%

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

   7. Simplified 20.4%

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

   8. Taylor expanded in y around inf 20.5%

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

      1. associate-*r* 20.5%

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

      2. neg-mul-1 20.5%

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

      3. *-commutative 20.5%

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

   10. Simplified 20.5%

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

   if -2.1000000000000001e85 < y < -1.5e-22 or 1.05e-10 < y

   1. Initial program 97.8%

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

   2. Taylor expanded in b around inf 41.3%

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

      1. mul-1-neg 41.3%

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

      2. distribute-rgt-neg-out 41.3%

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

   4. Simplified 41.3%

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

   5. Taylor expanded in a around 0 15.9%

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

      1. mul-1-neg 15.9%

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

      2. unsub-neg 15.9%

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

   7. Simplified 15.9%

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

   8. Taylor expanded in a around inf 26.1%

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

      1. mul-1-neg 26.1%

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

      2. associate-*r* 26.7%

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

      3. distribute-lft-neg-in 26.7%

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

      4. mul-1-neg 26.7%

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

      5. *-commutative 26.7%

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

      6. associate-*r* 26.7%

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

      7. neg-mul-1 26.7%

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

   10. Simplified 26.7%

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

   if -1.5e-22 < y < -1.8e-101

   1. Initial program 93.2%

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

   2. Taylor expanded in y around 0 65.8%

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

      1. sub-neg 65.8%

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

      2. sub-neg 65.8%

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

      3. neg-mul-1 65.8%

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

      4. log1p-def 79.4%

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

      5. neg-mul-1 79.4%

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

      6. sub-neg 79.4%

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

   4. Simplified 79.4%

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

   5. Taylor expanded in b around 0 11.5%

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

   6. Taylor expanded in z around 0 10.6%

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

      1. neg-mul-1 10.6%

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

      2. distribute-rgt-neg-in 10.6%

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

   8. Simplified 10.6%

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

   9. Taylor expanded in a around inf 37.6%

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

       1. associate-*r* 37.6%

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

       2. neg-mul-1 37.6%

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

   11. Simplified 37.6%

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

   if -1.8e-101 < y < 1.05e-10

   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 83.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   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 40.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-101}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 11: 28.7% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+89}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-101}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* a (- b)))))
   (if (<= y -1.7e+89)
     (* (- t) (* x y))
     (if (<= y -3.5e-24)
       t_1
       (if (<= y -1.8e-101) (* a (* x (- z))) (if (<= y 2.2e-12) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (a * -b);
	double tmp;
	if (y <= -1.7e+89) {
		tmp = -t * (x * y);
	} else if (y <= -3.5e-24) {
		tmp = t_1;
	} else if (y <= -1.8e-101) {
		tmp = a * (x * -z);
	} else if (y <= 2.2e-12) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (a * -b)
    if (y <= (-1.7d+89)) then
        tmp = -t * (x * y)
    else if (y <= (-3.5d-24)) then
        tmp = t_1
    else if (y <= (-1.8d-101)) then
        tmp = a * (x * -z)
    else if (y <= 2.2d-12) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (a * -b);
	double tmp;
	if (y <= -1.7e+89) {
		tmp = -t * (x * y);
	} else if (y <= -3.5e-24) {
		tmp = t_1;
	} else if (y <= -1.8e-101) {
		tmp = a * (x * -z);
	} else if (y <= 2.2e-12) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (a * -b)
	tmp = 0
	if y <= -1.7e+89:
		tmp = -t * (x * y)
	elif y <= -3.5e-24:
		tmp = t_1
	elif y <= -1.8e-101:
		tmp = a * (x * -z)
	elif y <= 2.2e-12:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(a * Float64(-b)))
	tmp = 0.0
	if (y <= -1.7e+89)
		tmp = Float64(Float64(-t) * Float64(x * y));
	elseif (y <= -3.5e-24)
		tmp = t_1;
	elseif (y <= -1.8e-101)
		tmp = Float64(a * Float64(x * Float64(-z)));
	elseif (y <= 2.2e-12)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (a * -b);
	tmp = 0.0;
	if (y <= -1.7e+89)
		tmp = -t * (x * y);
	elseif (y <= -3.5e-24)
		tmp = t_1;
	elseif (y <= -1.8e-101)
		tmp = a * (x * -z);
	elseif (y <= 2.2e-12)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+89], N[((-t) * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-24], t$95$1, If[LessEqual[y, -1.8e-101], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e-12], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7000000000000001e89

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. distribute-lft-neg-out 71.1%

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

      3. *-commutative 71.1%

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

   4. Simplified 71.1%

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

   5. Taylor expanded in y around 0 20.4%

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

      1. mul-1-neg 20.4%

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

      2. unsub-neg 20.4%

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

      3. *-commutative 20.4%

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

   7. Simplified 20.4%

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

   8. Taylor expanded in y around inf 22.6%

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

      1. associate-*r* 22.6%

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

      2. neg-mul-1 22.6%

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

   10. Simplified 22.6%

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

   if -1.7000000000000001e89 < y < -3.4999999999999996e-24 or 2.19999999999999992e-12 < y

   1. Initial program 97.8%

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

   2. Taylor expanded in b around inf 41.3%

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

      1. mul-1-neg 41.3%

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

      2. distribute-rgt-neg-out 41.3%

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

   4. Simplified 41.3%

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

   5. Taylor expanded in a around 0 15.9%

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

      1. mul-1-neg 15.9%

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

      2. unsub-neg 15.9%

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

   7. Simplified 15.9%

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

   8. Taylor expanded in a around inf 26.1%

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

      1. mul-1-neg 26.1%

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

      2. associate-*r* 26.7%

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

      3. distribute-lft-neg-in 26.7%

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

      4. mul-1-neg 26.7%

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

      5. *-commutative 26.7%

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

      6. associate-*r* 26.7%

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

      7. neg-mul-1 26.7%

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

   10. Simplified 26.7%

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

   if -3.4999999999999996e-24 < y < -1.8e-101

   1. Initial program 93.2%

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

   2. Taylor expanded in y around 0 65.8%

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

      1. sub-neg 65.8%

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

      2. sub-neg 65.8%

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

      3. neg-mul-1 65.8%

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

      4. log1p-def 79.4%

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

      5. neg-mul-1 79.4%

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

      6. sub-neg 79.4%

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

   4. Simplified 79.4%

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

   5. Taylor expanded in b around 0 11.5%

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

   6. Taylor expanded in z around 0 10.6%

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

      1. neg-mul-1 10.6%

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

      2. distribute-rgt-neg-in 10.6%

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

   8. Simplified 10.6%

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

   9. Taylor expanded in a around inf 37.6%

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

       1. associate-*r* 37.6%

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

       2. neg-mul-1 37.6%

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

   11. Simplified 37.6%

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

   if -1.8e-101 < y < 2.19999999999999992e-12

   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 83.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   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 40.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+89}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-101}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 12: 29.2% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+86}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-100}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(1 - z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.5e+86)
   (* (- t) (* x y))
   (if (<= y -7.5e-100)
     (* a (* x (- b)))
     (if (<= y 1.2e-12) (* x (- 1.0 (* z a))) (* x (* a (- b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.5e+86) {
		tmp = -t * (x * y);
	} else if (y <= -7.5e-100) {
		tmp = a * (x * -b);
	} else if (y <= 1.2e-12) {
		tmp = x * (1.0 - (z * a));
	} else {
		tmp = x * (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 <= (-7.5d+86)) then
        tmp = -t * (x * y)
    else if (y <= (-7.5d-100)) then
        tmp = a * (x * -b)
    else if (y <= 1.2d-12) then
        tmp = x * (1.0d0 - (z * a))
    else
        tmp = x * (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 <= -7.5e+86) {
		tmp = -t * (x * y);
	} else if (y <= -7.5e-100) {
		tmp = a * (x * -b);
	} else if (y <= 1.2e-12) {
		tmp = x * (1.0 - (z * a));
	} else {
		tmp = x * (a * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.5e+86:
		tmp = -t * (x * y)
	elif y <= -7.5e-100:
		tmp = a * (x * -b)
	elif y <= 1.2e-12:
		tmp = x * (1.0 - (z * a))
	else:
		tmp = x * (a * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.5e+86)
		tmp = Float64(Float64(-t) * Float64(x * y));
	elseif (y <= -7.5e-100)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= 1.2e-12)
		tmp = Float64(x * Float64(1.0 - Float64(z * a)));
	else
		tmp = Float64(x * Float64(a * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.5e+86)
		tmp = -t * (x * y);
	elseif (y <= -7.5e-100)
		tmp = a * (x * -b);
	elseif (y <= 1.2e-12)
		tmp = x * (1.0 - (z * a));
	else
		tmp = x * (a * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.5e+86], N[((-t) * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-100], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-12], N[(x * N[(1.0 - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.4999999999999997e86

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. distribute-lft-neg-out 71.1%

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

      3. *-commutative 71.1%

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

   4. Simplified 71.1%

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

   5. Taylor expanded in y around 0 20.4%

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

      1. mul-1-neg 20.4%

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

      2. unsub-neg 20.4%

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

      3. *-commutative 20.4%

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

   7. Simplified 20.4%

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

   8. Taylor expanded in y around inf 22.6%

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

      1. associate-*r* 22.6%

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

      2. neg-mul-1 22.6%

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

   10. Simplified 22.6%

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

   if -7.4999999999999997e86 < y < -7.50000000000000015e-100

   1. Initial program 94.1%

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

   2. Taylor expanded in b around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. distribute-rgt-neg-out 53.9%

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

   4. Simplified 53.9%

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

   5. Taylor expanded in a around 0 21.4%

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

      1. mul-1-neg 21.4%

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

      2. unsub-neg 21.4%

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

   7. Simplified 21.4%

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

   8. Taylor expanded in a around inf 26.5%

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

   if -7.50000000000000015e-100 < y < 1.19999999999999994e-12

   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 y around 0 85.8%

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

      1. sub-neg 85.8%

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

      2. sub-neg 85.8%

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

      3. neg-mul-1 85.8%

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

      4. log1p-def 90.3%

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

      5. neg-mul-1 90.3%

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

      6. sub-neg 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in b around 0 42.5%

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

   6. Taylor expanded in z around 0 42.4%

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

      1. neg-mul-1 42.4%

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

      2. distribute-rgt-neg-in 42.4%

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

   8. Simplified 42.4%

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

   9. Taylor expanded in x around 0 42.4%

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

       1. mul-1-neg 42.4%

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

       2. unsub-neg 42.4%

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

   11. Simplified 42.4%

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

   if 1.19999999999999994e-12 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in b around inf 38.6%

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

      1. mul-1-neg 38.6%

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

      2. distribute-rgt-neg-out 38.6%

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

   4. Simplified 38.6%

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

   5. Taylor expanded in a around 0 14.0%

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

      1. mul-1-neg 14.0%

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

      2. unsub-neg 14.0%

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

   7. Simplified 14.0%

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

   8. Taylor expanded in a around inf 26.1%

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

      1. mul-1-neg 26.1%

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

      2. associate-*r* 27.1%

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

      3. distribute-lft-neg-in 27.1%

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

      4. mul-1-neg 27.1%

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

      5. *-commutative 27.1%

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

      6. associate-*r* 27.1%

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

      7. neg-mul-1 27.1%

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

   10. Simplified 27.1%

       \[\leadsto \color{blue}{x \cdot \left(\left(-a\right) \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+86}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-100}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(1 - z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 13: 30.6% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y \cdot t\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+103}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (* y t)))))
   (if (<= t -8.5e+237)
     t_1
     (if (<= t -2.05e+97)
       (* a (* x (- z)))
       (if (<= t 1.85e+103) (- x (* a (* x b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 - (y * t));
	double tmp;
	if (t <= -8.5e+237) {
		tmp = t_1;
	} else if (t <= -2.05e+97) {
		tmp = a * (x * -z);
	} else if (t <= 1.85e+103) {
		tmp = x - (a * (x * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y * t))
    if (t <= (-8.5d+237)) then
        tmp = t_1
    else if (t <= (-2.05d+97)) then
        tmp = a * (x * -z)
    else if (t <= 1.85d+103) then
        tmp = x - (a * (x * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 - (y * t));
	double tmp;
	if (t <= -8.5e+237) {
		tmp = t_1;
	} else if (t <= -2.05e+97) {
		tmp = a * (x * -z);
	} else if (t <= 1.85e+103) {
		tmp = x - (a * (x * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (1.0 - (y * t))
	tmp = 0
	if t <= -8.5e+237:
		tmp = t_1
	elif t <= -2.05e+97:
		tmp = a * (x * -z)
	elif t <= 1.85e+103:
		tmp = x - (a * (x * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(1.0 - Float64(y * t)))
	tmp = 0.0
	if (t <= -8.5e+237)
		tmp = t_1;
	elseif (t <= -2.05e+97)
		tmp = Float64(a * Float64(x * Float64(-z)));
	elseif (t <= 1.85e+103)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (1.0 - (y * t));
	tmp = 0.0;
	if (t <= -8.5e+237)
		tmp = t_1;
	elseif (t <= -2.05e+97)
		tmp = a * (x * -z);
	elseif (t <= 1.85e+103)
		tmp = x - (a * (x * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+237], t$95$1, If[LessEqual[t, -2.05e+97], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+103], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.4999999999999994e237 or 1.85000000000000016e103 < t

   1. Initial program 96.3%

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

   2. Taylor expanded in t around inf 82.4%

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

      1. mul-1-neg 82.4%

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

      2. distribute-lft-neg-out 82.4%

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

      3. *-commutative 82.4%

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

   4. Simplified 82.4%

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

   5. Taylor expanded in y around 0 36.4%

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

      1. mul-1-neg 36.4%

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

      2. unsub-neg 36.4%

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

      3. *-commutative 36.4%

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

   7. Simplified 36.4%

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

   if -8.4999999999999994e237 < t < -2.04999999999999994e97

   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 51.7%

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

      1. sub-neg 51.7%

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

      2. sub-neg 51.7%

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

      3. neg-mul-1 51.7%

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

      4. log1p-def 55.5%

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

      5. neg-mul-1 55.5%

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

      6. sub-neg 55.5%

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

   4. Simplified 55.5%

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

   5. Taylor expanded in b around 0 8.1%

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

   6. Taylor expanded in z around 0 7.7%

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

      1. neg-mul-1 7.7%

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

      2. distribute-rgt-neg-in 7.7%

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

   8. Simplified 7.7%

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

   9. Taylor expanded in a around inf 36.6%

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

       1. associate-*r* 36.6%

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

       2. neg-mul-1 36.6%

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

   11. Simplified 36.6%

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

   if -2.04999999999999994e97 < t < 1.85000000000000016e103

   1. Initial program 96.7%

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

   2. Taylor expanded in b around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. distribute-rgt-neg-out 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in a around 0 34.5%

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

      1. mul-1-neg 34.5%

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

      2. unsub-neg 34.5%

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

   7. Simplified 34.5%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+237}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+103}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \]

Alternative 14: 29.0% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-101} \lor \neg \left(y \leq 4.8 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.8e+87)
   (* x (* y (- t)))
   (if (or (<= y -1.7e-101) (not (<= y 4.8e-11))) (* x (* a (- b))) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.8e+87) {
		tmp = x * (y * -t);
	} else if ((y <= -1.7e-101) || !(y <= 4.8e-11)) {
		tmp = x * (a * -b);
	} 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 <= (-4.8d+87)) then
        tmp = x * (y * -t)
    else if ((y <= (-1.7d-101)) .or. (.not. (y <= 4.8d-11))) then
        tmp = x * (a * -b)
    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 <= -4.8e+87) {
		tmp = x * (y * -t);
	} else if ((y <= -1.7e-101) || !(y <= 4.8e-11)) {
		tmp = x * (a * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.8e+87:
		tmp = x * (y * -t)
	elif (y <= -1.7e-101) or not (y <= 4.8e-11):
		tmp = x * (a * -b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.8e+87)
		tmp = Float64(x * Float64(y * Float64(-t)));
	elseif ((y <= -1.7e-101) || !(y <= 4.8e-11))
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.8e+87)
		tmp = x * (y * -t);
	elseif ((y <= -1.7e-101) || ~((y <= 4.8e-11)))
		tmp = x * (a * -b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.8e+87], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.7e-101], N[Not[LessEqual[y, 4.8e-11]], $MachinePrecision]], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < -4.79999999999999963e87

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. distribute-lft-neg-out 71.1%

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

      3. *-commutative 71.1%

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

   4. Simplified 71.1%

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

   5. Taylor expanded in y around 0 20.4%

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

      1. mul-1-neg 20.4%

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

      2. unsub-neg 20.4%

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

      3. *-commutative 20.4%

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

   7. Simplified 20.4%

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

   8. Taylor expanded in y around inf 20.5%

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

      1. associate-*r* 20.5%

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

      2. neg-mul-1 20.5%

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

      3. *-commutative 20.5%

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

   10. Simplified 20.5%

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

   if -4.79999999999999963e87 < y < -1.69999999999999995e-101 or 4.8000000000000002e-11 < y

   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 b around inf 44.6%

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

      1. mul-1-neg 44.6%

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

      2. distribute-rgt-neg-out 44.6%

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

   4. Simplified 44.6%

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

   5. Taylor expanded in a around 0 16.1%

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

      1. mul-1-neg 16.1%

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

      2. unsub-neg 16.1%

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

   7. Simplified 16.1%

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

   8. Taylor expanded in a around inf 25.8%

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

      1. mul-1-neg 25.8%

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

      2. associate-*r* 25.5%

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

      3. distribute-lft-neg-in 25.5%

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

      4. mul-1-neg 25.5%

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

      5. *-commutative 25.5%

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

      6. associate-*r* 25.5%

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

      7. neg-mul-1 25.5%

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

   10. Simplified 25.5%

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

   if -1.69999999999999995e-101 < y < 4.8000000000000002e-11

   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 83.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   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 40.5%

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

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-101} \lor \neg \left(y \leq 4.8 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 28.7% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+87}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-101}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8e+87)
   (* (- t) (* x y))
   (if (<= y -1.2e-101)
     (* a (* x (- b)))
     (if (<= y 1.6e-12) x (* x (* a (- b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e+87) {
		tmp = -t * (x * y);
	} else if (y <= -1.2e-101) {
		tmp = a * (x * -b);
	} else if (y <= 1.6e-12) {
		tmp = x;
	} else {
		tmp = x * (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 <= (-8d+87)) then
        tmp = -t * (x * y)
    else if (y <= (-1.2d-101)) then
        tmp = a * (x * -b)
    else if (y <= 1.6d-12) then
        tmp = x
    else
        tmp = x * (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 <= -8e+87) {
		tmp = -t * (x * y);
	} else if (y <= -1.2e-101) {
		tmp = a * (x * -b);
	} else if (y <= 1.6e-12) {
		tmp = x;
	} else {
		tmp = x * (a * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8e+87:
		tmp = -t * (x * y)
	elif y <= -1.2e-101:
		tmp = a * (x * -b)
	elif y <= 1.6e-12:
		tmp = x
	else:
		tmp = x * (a * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8e+87)
		tmp = Float64(Float64(-t) * Float64(x * y));
	elseif (y <= -1.2e-101)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= 1.6e-12)
		tmp = x;
	else
		tmp = Float64(x * Float64(a * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8e+87)
		tmp = -t * (x * y);
	elseif (y <= -1.2e-101)
		tmp = a * (x * -b);
	elseif (y <= 1.6e-12)
		tmp = x;
	else
		tmp = x * (a * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8e+87], N[((-t) * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-101], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-12], x, N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.9999999999999997e87

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. distribute-lft-neg-out 71.1%

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

      3. *-commutative 71.1%

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

   4. Simplified 71.1%

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

   5. Taylor expanded in y around 0 20.4%

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

      1. mul-1-neg 20.4%

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

      2. unsub-neg 20.4%

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

      3. *-commutative 20.4%

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

   7. Simplified 20.4%

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

   8. Taylor expanded in y around inf 22.6%

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

      1. associate-*r* 22.6%

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

      2. neg-mul-1 22.6%

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

   10. Simplified 22.6%

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

   if -7.9999999999999997e87 < y < -1.2e-101

   1. Initial program 94.5%

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

   2. Taylor expanded in b around inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. distribute-rgt-neg-out 56.5%

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

   4. Simplified 56.5%

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

   5. Taylor expanded in a around 0 20.4%

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

      1. mul-1-neg 20.4%

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

      2. unsub-neg 20.4%

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

   7. Simplified 20.4%

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

   8. Taylor expanded in a around inf 25.2%

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

   if -1.2e-101 < y < 1.6e-12

   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 83.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   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 40.5%

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

   if 1.6e-12 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in b around inf 38.6%

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

      1. mul-1-neg 38.6%

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

      2. distribute-rgt-neg-out 38.6%

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

   4. Simplified 38.6%

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

   5. Taylor expanded in a around 0 14.0%

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

      1. mul-1-neg 14.0%

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

      2. unsub-neg 14.0%

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

   7. Simplified 14.0%

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

   8. Taylor expanded in a around inf 26.1%

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

      1. mul-1-neg 26.1%

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

      2. associate-*r* 27.1%

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

      3. distribute-lft-neg-in 27.1%

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

      4. mul-1-neg 27.1%

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

      5. *-commutative 27.1%

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

      6. associate-*r* 27.1%

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

      7. neg-mul-1 27.1%

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

   10. Simplified 27.1%

       \[\leadsto \color{blue}{x \cdot \left(\left(-a\right) \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+87}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-101}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 16: 27.4% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-101} \lor \neg \left(y \leq 3.5 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.05e-101) (not (<= y 3.5e-10))) (* x (* y (- t))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.05e-101) || !(y <= 3.5e-10)) {
		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 <= (-2.05d-101)) .or. (.not. (y <= 3.5d-10))) 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 <= -2.05e-101) || !(y <= 3.5e-10)) {
		tmp = x * (y * -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.05e-101) or not (y <= 3.5e-10):
		tmp = x * (y * -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.05e-101) || !(y <= 3.5e-10))
		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 <= -2.05e-101) || ~((y <= 3.5e-10)))
		tmp = x * (y * -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.05e-101], N[Not[LessEqual[y, 3.5e-10]], $MachinePrecision]], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.05000000000000013e-101 or 3.4999999999999998e-10 < y

   1. Initial program 97.3%

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

   2. Taylor expanded in t around inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. distribute-lft-neg-out 60.6%

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

      3. *-commutative 60.6%

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

   4. Simplified 60.6%

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

   5. Taylor expanded in y around 0 17.3%

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

      1. mul-1-neg 17.3%

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

      2. unsub-neg 17.3%

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

      3. *-commutative 17.3%

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

   7. Simplified 17.3%

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

   8. Taylor expanded in y around inf 17.4%

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

      1. associate-*r* 17.4%

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

      2. neg-mul-1 17.4%

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

      3. *-commutative 17.4%

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

   10. Simplified 17.4%

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

   if -2.05000000000000013e-101 < y < 3.4999999999999998e-10

   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 83.9%

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

      1. mul-1-neg 83.9%

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

      2. distribute-rgt-neg-out 83.9%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in a around 0 40.2%

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

4. Final simplification 27.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-101} \lor \neg \left(y \leq 3.5 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 21.6% accurate, 34.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-17} \lor \neg \left(a \leq 3.4 \cdot 10^{+197}\right):\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -5.8e-17) (not (<= a 3.4e+197))) (* t (* x y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -5.8e-17) || !(a <= 3.4e+197)) {
		tmp = t * (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-5.8d-17)) .or. (.not. (a <= 3.4d+197))) then
        tmp = t * (x * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -5.8e-17) || !(a <= 3.4e+197)) {
		tmp = t * (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -5.8e-17) or not (a <= 3.4e+197):
		tmp = t * (x * y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -5.8e-17) || !(a <= 3.4e+197))
		tmp = Float64(t * Float64(x * y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -5.8e-17) || ~((a <= 3.4e+197)))
		tmp = t * (x * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -5.8e-17], N[Not[LessEqual[a, 3.4e+197]], $MachinePrecision]], N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -5.8000000000000006e-17 or 3.40000000000000017e197 < a

   1. Initial program 91.8%

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

   2. Taylor expanded in t around inf 36.3%

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

      1. mul-1-neg 36.3%

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

      2. distribute-lft-neg-out 36.3%

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

      3. *-commutative 36.3%

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

   4. Simplified 36.3%

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

   5. Taylor expanded in y around 0 10.8%

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

      1. mul-1-neg 10.8%

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

      2. unsub-neg 10.8%

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

      3. *-commutative 10.8%

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

   7. Simplified 10.8%

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

   8. Taylor expanded in y around inf 22.3%

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

      1. associate-*r* 22.3%

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

      2. neg-mul-1 22.3%

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

      3. *-commutative 22.3%

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

   10. Simplified 22.3%

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

       1. expm1-log1p-u 19.4%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot \left(-t\right)\right)\right)\right)} \]

       2. expm1-udef 31.1%

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

       3. *-commutative 31.1%

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

       4. *-commutative 31.1%

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

       5. associate-*l* 31.1%

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

       6. add-sqr-sqrt 19.6%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)} \cdot \left(y \cdot x\right)\right)} - 1 \]

       7. sqrt-unprod 29.6%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}} \cdot \left(y \cdot x\right)\right)} - 1 \]

       8. sqr-neg 29.6%

          \[\leadsto e^{\mathsf{log1p}\left(\sqrt{\color{blue}{t \cdot t}} \cdot \left(y \cdot x\right)\right)} - 1 \]

       9. sqrt-unprod 11.4%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)} \cdot \left(y \cdot x\right)\right)} - 1 \]

       10. add-sqr-sqrt 29.9%

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

   12. Applied egg-rr 29.9%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(t \cdot \left(y \cdot x\right)\right)} - 1} \]
   13. Step-by-step derivation

       1. expm1-def 17.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot x\right)\right)\right)} \]

       2. expm1-log1p 17.5%

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

       3. *-commutative 17.5%

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

   14. Simplified 17.5%

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

   if -5.8000000000000006e-17 < a < 3.40000000000000017e197

   1. Initial program 98.8%

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

   2. Taylor expanded in b around inf 54.1%

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

      1. mul-1-neg 54.1%

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

      2. distribute-rgt-neg-out 54.1%

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

   4. Simplified 54.1%

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

   5. Taylor expanded in a around 0 26.7%

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

4. Final simplification 23.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-17} \lor \neg \left(a \leq 3.4 \cdot 10^{+197}\right):\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 21.5% accurate, 34.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-13}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+197}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.8e-13) (* t (* x y)) (if (<= a 4.2e+197) x (* x (* y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.8e-13) {
		tmp = t * (x * y);
	} else if (a <= 4.2e+197) {
		tmp = x;
	} else {
		tmp = x * (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 (a <= (-5.8d-13)) then
        tmp = t * (x * y)
    else if (a <= 4.2d+197) then
        tmp = x
    else
        tmp = x * (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 (a <= -5.8e-13) {
		tmp = t * (x * y);
	} else if (a <= 4.2e+197) {
		tmp = x;
	} else {
		tmp = x * (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.8e-13:
		tmp = t * (x * y)
	elif a <= 4.2e+197:
		tmp = x
	else:
		tmp = x * (y * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.8e-13)
		tmp = Float64(t * Float64(x * y));
	elseif (a <= 4.2e+197)
		tmp = x;
	else
		tmp = Float64(x * Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.8e-13)
		tmp = t * (x * y);
	elseif (a <= 4.2e+197)
		tmp = x;
	else
		tmp = x * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.8e-13], N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+197], x, N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.7999999999999995e-13

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf 37.5%

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

      1. mul-1-neg 37.5%

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

      2. distribute-lft-neg-out 37.5%

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

      3. *-commutative 37.5%

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

   4. Simplified 37.5%

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

   5. Taylor expanded in y around 0 13.0%

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

      1. mul-1-neg 13.0%

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

      2. unsub-neg 13.0%

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

      3. *-commutative 13.0%

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

   7. Simplified 13.0%

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

   8. Taylor expanded in y around inf 16.3%

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

      1. associate-*r* 16.3%

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

      2. neg-mul-1 16.3%

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

      3. *-commutative 16.3%

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

   10. Simplified 16.3%

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

       1. expm1-log1p-u 12.6%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot \left(-t\right)\right)\right)\right)} \]

       2. expm1-udef 25.0%

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

       3. *-commutative 25.0%

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

       4. *-commutative 25.0%

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

       5. associate-*l* 25.0%

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

       6. add-sqr-sqrt 16.3%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)} \cdot \left(y \cdot x\right)\right)} - 1 \]

       7. sqrt-unprod 23.0%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}} \cdot \left(y \cdot x\right)\right)} - 1 \]

       8. sqr-neg 23.0%

          \[\leadsto e^{\mathsf{log1p}\left(\sqrt{\color{blue}{t \cdot t}} \cdot \left(y \cdot x\right)\right)} - 1 \]

       9. sqrt-unprod 8.4%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)} \cdot \left(y \cdot x\right)\right)} - 1 \]

       10. add-sqr-sqrt 23.2%

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

   12. Applied egg-rr 23.2%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(t \cdot \left(y \cdot x\right)\right)} - 1} \]
   13. Step-by-step derivation

       1. expm1-def 12.4%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot x\right)\right)\right)} \]

       2. expm1-log1p 12.7%

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

       3. *-commutative 12.7%

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

   14. Simplified 12.7%

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

   if -5.7999999999999995e-13 < a < 4.20000000000000013e197

   1. Initial program 98.8%

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

   2. Taylor expanded in b around inf 54.1%

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

      1. mul-1-neg 54.1%

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

      2. distribute-rgt-neg-out 54.1%

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

   4. Simplified 54.1%

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

   5. Taylor expanded in a around 0 26.7%

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

   if 4.20000000000000013e197 < a

   1. Initial program 90.1%

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

   2. Taylor expanded in t around inf 32.7%

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

      1. mul-1-neg 32.7%

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

      2. distribute-lft-neg-out 32.7%

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

      3. *-commutative 32.7%

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

   4. Simplified 32.7%

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

   5. Taylor expanded in y around 0 3.6%

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

      1. mul-1-neg 3.6%

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

      2. unsub-neg 3.6%

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

      3. *-commutative 3.6%

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

   7. Simplified 3.6%

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

   8. Taylor expanded in y around inf 41.6%

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

      1. associate-*r* 41.6%

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

      2. neg-mul-1 41.6%

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

      3. *-commutative 41.6%

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

   10. Simplified 41.6%

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

       1. expm1-log1p-u 40.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot \left(-t\right)\right)\right)\right)} \]

       2. expm1-udef 50.5%

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

       3. *-commutative 50.5%

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

       4. *-commutative 50.5%

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

       5. associate-*l* 50.5%

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

       6. add-sqr-sqrt 30.2%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)} \cdot \left(y \cdot x\right)\right)} - 1 \]

       7. sqrt-unprod 50.2%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}} \cdot \left(y \cdot x\right)\right)} - 1 \]

       8. sqr-neg 50.2%

          \[\leadsto e^{\mathsf{log1p}\left(\sqrt{\color{blue}{t \cdot t}} \cdot \left(y \cdot x\right)\right)} - 1 \]

       9. sqrt-unprod 20.7%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)} \cdot \left(y \cdot x\right)\right)} - 1 \]

       10. add-sqr-sqrt 51.1%

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

   12. Applied egg-rr 51.1%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(t \cdot \left(y \cdot x\right)\right)} - 1} \]
   13. Step-by-step derivation

       1. expm1-def 32.4%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot x\right)\right)\right)} \]

       2. expm1-log1p 32.5%

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

       3. associate-*r* 46.3%

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

       4. *-commutative 46.3%

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

   14. Simplified 46.3%

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

4. Final simplification 24.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-13}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+197}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 19: 19.9% 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 96.5%

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

2. Taylor expanded in b around inf 59.5%

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

   1. mul-1-neg 59.5%

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

   2. distribute-rgt-neg-out 59.5%

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

4. Simplified 59.5%

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

5. Taylor expanded in a around 0 19.8%

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

6. Final simplification 19.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023308 
(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))))))