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

Percentage Accurate: 96.1% → 99.6%

Time: 19.4s

Alternatives: 19

Speedup: 1.0×

• 20.5% 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: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.8× speedup

Math

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

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 97.7%

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

   1. fma-def 97.7%

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

   2. sub-neg 97.7%

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

   3. log1p-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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(((a * (log((1.0d0 - z)) - b)) + (y * (log(z) - t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 97.7%

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

Alternative 3: 90.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4050000000 \lor \neg \left(y \leq 2.2 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-y \cdot t\right) - a \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4050000000.0) (not (<= y 2.2e+31)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (- (- (* y t)) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4050000000.0) || !(y <= 2.2e+31)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((-(y * t) - (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 <= (-4050000000.0d0)) .or. (.not. (y <= 2.2d+31))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((-(y * t) - (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 <= -4050000000.0) || !(y <= 2.2e+31)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((-(y * t) - (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4050000000.0) or not (y <= 2.2e+31):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((-(y * t) - (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4050000000.0) || !(y <= 2.2e+31))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(Float64(-Float64(y * t)) - Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4050000000.0) || ~((y <= 2.2e+31)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((-(y * t) - (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4050000000.0], N[Not[LessEqual[y, 2.2e+31]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[((-N[(y * t), $MachinePrecision]) - N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.05e9 or 2.2000000000000001e31 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in a around 0 95.5%

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

   if -4.05e9 < y < 2.2000000000000001e31

   1. Initial program 96.6%

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

      1. fma-def 96.6%

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

      2. sub-neg 96.6%

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

      3. log1p-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 95.3%

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

   5. Taylor expanded in t around inf 94.7%

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

      1. neg-mul-1 54.1%

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

   7. Simplified 94.7%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4050000000 \lor \neg \left(y \leq 2.2 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-y \cdot t\right) - a \cdot b}\\ \end{array} \]

Alternative 4: 95.6% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. fma-def 97.7%

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

   2. sub-neg 97.7%

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

   3. log1p-def 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in z around 0 96.9%

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

5. Final simplification 96.9%

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

Alternative 5: 75.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ t_2 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot e^{-y \cdot t}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* a (- (- z) b))))) (t_2 (* x (pow z y))))
   (if (<= y -2.6e+64)
     t_2
     (if (<= y 2.7e-15)
       t_1
       (if (<= y 6.2e+23)
         (* x (exp (- (* y t))))
         (if (<= y 1.7e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((a * (-z - b)));
	double t_2 = x * pow(z, y);
	double tmp;
	if (y <= -2.6e+64) {
		tmp = t_2;
	} else if (y <= 2.7e-15) {
		tmp = t_1;
	} else if (y <= 6.2e+23) {
		tmp = x * exp(-(y * t));
	} else if (y <= 1.7e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * exp((a * (-z - b)))
    t_2 = x * (z ** y)
    if (y <= (-2.6d+64)) then
        tmp = t_2
    else if (y <= 2.7d-15) then
        tmp = t_1
    else if (y <= 6.2d+23) then
        tmp = x * exp(-(y * t))
    else if (y <= 1.7d+37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((a * (-z - b)));
	double t_2 = x * Math.pow(z, y);
	double tmp;
	if (y <= -2.6e+64) {
		tmp = t_2;
	} else if (y <= 2.7e-15) {
		tmp = t_1;
	} else if (y <= 6.2e+23) {
		tmp = x * Math.exp(-(y * t));
	} else if (y <= 1.7e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((a * (-z - b)))
	t_2 = x * math.pow(z, y)
	tmp = 0
	if y <= -2.6e+64:
		tmp = t_2
	elif y <= 2.7e-15:
		tmp = t_1
	elif y <= 6.2e+23:
		tmp = x * math.exp(-(y * t))
	elif y <= 1.7e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))))
	t_2 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -2.6e+64)
		tmp = t_2;
	elseif (y <= 2.7e-15)
		tmp = t_1;
	elseif (y <= 6.2e+23)
		tmp = Float64(x * exp(Float64(-Float64(y * t))));
	elseif (y <= 1.7e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((a * (-z - b)));
	t_2 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -2.6e+64)
		tmp = t_2;
	elseif (y <= 2.7e-15)
		tmp = t_1;
	elseif (y <= 6.2e+23)
		tmp = x * exp(-(y * t));
	elseif (y <= 1.7e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+64], t$95$2, If[LessEqual[y, 2.7e-15], t$95$1, If[LessEqual[y, 6.2e+23], N[(x * N[Exp[(-N[(y * t), $MachinePrecision])], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.59999999999999997e64 or 1.70000000000000003e37 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 96.1%

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

   3. Taylor expanded in t around 0 78.3%

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

   if -2.59999999999999997e64 < y < 2.70000000000000009e-15 or 6.19999999999999941e23 < y < 1.70000000000000003e37

   1. Initial program 96.6%

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

   2. Taylor expanded in y around 0 82.7%

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

      1. sub-neg 82.7%

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

      2. neg-mul-1 82.7%

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

      3. log1p-def 88.1%

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

      4. neg-mul-1 88.1%

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

   4. Simplified 88.1%

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

   5. Taylor expanded in z around 0 88.1%

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

      1. neg-mul-1 88.1%

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

      2. unsub-neg 88.1%

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

      3. neg-mul-1 88.1%

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

   7. Simplified 88.1%

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

   if 2.70000000000000009e-15 < y < 6.19999999999999941e23

   1. Initial program 91.1%

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

   2. Taylor expanded in a around 0 82.2%

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

   3. Taylor expanded in t around inf 74.0%

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

      1. neg-mul-1 74.0%

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

   5. Simplified 74.0%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+64}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot e^{-y \cdot t}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+37}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 6: 72.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-17}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+24}:\\ \;\;\;\;x \cdot e^{-y \cdot t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\frac{\left(a \cdot a\right) \cdot \left(\left(b \cdot b\right) \cdot \left(x \cdot \left(-x\right)\right)\right)}{x + a \cdot \left(x \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -4.2e+14)
     t_1
     (if (<= y 9.5e-17)
       (* x (exp (* a (- b))))
       (if (<= y 1.12e+24)
         (* x (exp (- (* y t))))
         (if (<= y 2e+31)
           (/ (* (* a a) (* (* b b) (* x (- x)))) (+ 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 * pow(z, y);
	double tmp;
	if (y <= -4.2e+14) {
		tmp = t_1;
	} else if (y <= 9.5e-17) {
		tmp = x * exp((a * -b));
	} else if (y <= 1.12e+24) {
		tmp = x * exp(-(y * t));
	} else if (y <= 2e+31) {
		tmp = ((a * a) * ((b * b) * (x * -x))) / (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 * (z ** y)
    if (y <= (-4.2d+14)) then
        tmp = t_1
    else if (y <= 9.5d-17) then
        tmp = x * exp((a * -b))
    else if (y <= 1.12d+24) then
        tmp = x * exp(-(y * t))
    else if (y <= 2d+31) then
        tmp = ((a * a) * ((b * b) * (x * -x))) / (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 * Math.pow(z, y);
	double tmp;
	if (y <= -4.2e+14) {
		tmp = t_1;
	} else if (y <= 9.5e-17) {
		tmp = x * Math.exp((a * -b));
	} else if (y <= 1.12e+24) {
		tmp = x * Math.exp(-(y * t));
	} else if (y <= 2e+31) {
		tmp = ((a * a) * ((b * b) * (x * -x))) / (x + (a * (x * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -4.2e+14:
		tmp = t_1
	elif y <= 9.5e-17:
		tmp = x * math.exp((a * -b))
	elif y <= 1.12e+24:
		tmp = x * math.exp(-(y * t))
	elif y <= 2e+31:
		tmp = ((a * a) * ((b * b) * (x * -x))) / (x + (a * (x * b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -4.2e+14)
		tmp = t_1;
	elseif (y <= 9.5e-17)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif (y <= 1.12e+24)
		tmp = Float64(x * exp(Float64(-Float64(y * t))));
	elseif (y <= 2e+31)
		tmp = Float64(Float64(Float64(a * a) * Float64(Float64(b * b) * Float64(x * Float64(-x)))) / 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 * (z ^ y);
	tmp = 0.0;
	if (y <= -4.2e+14)
		tmp = t_1;
	elseif (y <= 9.5e-17)
		tmp = x * exp((a * -b));
	elseif (y <= 1.12e+24)
		tmp = x * exp(-(y * t));
	elseif (y <= 2e+31)
		tmp = ((a * a) * ((b * b) * (x * -x))) / (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[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+14], t$95$1, If[LessEqual[y, 9.5e-17], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+24], N[(x * N[Exp[(-N[(y * t), $MachinePrecision])], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+31], N[(N[(N[(a * a), $MachinePrecision] * N[(N[(b * b), $MachinePrecision] * N[(x * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2e14 or 1.9999999999999999e31 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in a around 0 95.4%

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

   3. Taylor expanded in t around 0 77.0%

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

   if -4.2e14 < y < 9.50000000000000029e-17

   1. Initial program 97.1%

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

   2. Taylor expanded in b around inf 82.3%

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

      1. mul-1-neg 82.3%

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

      2. *-commutative 82.3%

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

      3. distribute-rgt-neg-in 82.3%

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

   4. Simplified 82.3%

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

   if 9.50000000000000029e-17 < y < 1.12e24

   1. Initial program 91.1%

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

   2. Taylor expanded in a around 0 82.2%

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

   3. Taylor expanded in t around inf 74.0%

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

      1. neg-mul-1 74.0%

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

   5. Simplified 74.0%

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

   if 1.12e24 < y < 1.9999999999999999e31

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in b around 0 5.7%

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

      1. +-commutative 5.7%

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

      2. mul-1-neg 5.7%

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

      3. unsub-neg 5.7%

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

   7. Simplified 5.7%

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

      1. cancel-sign-sub-inv 5.7%

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

      2. flip-+ 100.0%

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

   9. Applied egg-rr 100.0%

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

   10. Taylor expanded in a around inf 100.0%

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

       1. mul-1-neg 100.0%

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

       2. unpow2 100.0%

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

       3. unpow2 100.0%

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

       4. unpow2 100.0%

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

   12. Simplified 100.0%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+14}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-17}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+24}:\\ \;\;\;\;x \cdot e^{-y \cdot t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\frac{\left(a \cdot a\right) \cdot \left(\left(b \cdot b\right) \cdot \left(x \cdot \left(-x\right)\right)\right)}{x + a \cdot \left(x \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 7: 83.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{+73}:\\ \;\;\;\;x \cdot e^{\left(-y \cdot t\right) - a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.55e+73) (* x (exp (- (- (* y t)) (* 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 <= 1.55e+73) {
		tmp = x * exp((-(y * t) - (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 <= 1.55d+73) then
        tmp = x * exp((-(y * t) - (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 <= 1.55e+73) {
		tmp = x * Math.exp((-(y * t) - (a * b)));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.55e+73:
		tmp = x * math.exp((-(y * t) - (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 <= 1.55e+73)
		tmp = Float64(x * exp(Float64(Float64(-Float64(y * t)) - Float64(a * 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 <= 1.55e+73)
		tmp = x * exp((-(y * t) - (a * b)));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.55e+73], N[(x * N[Exp[N[((-N[(y * t), $MachinePrecision]) - N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.55e73

   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. Step-by-step derivation

      1. fma-def 97.0%

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

      2. sub-neg 97.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 96.1%

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

   5. Taylor expanded in t around inf 87.9%

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

      1. neg-mul-1 54.8%

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

   7. Simplified 87.9%

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

   if 1.55e73 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 96.4%

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

   3. Taylor expanded in t around 0 80.3%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{+73}:\\ \;\;\;\;x \cdot e^{\left(-y \cdot t\right) - a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 8: 72.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+14} \lor \neg \left(y \leq 2.6 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.2e+14) (not (<= y 2.6e+31)))
   (* 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 <= -4.2e+14) || !(y <= 2.6e+31)) {
		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 <= (-4.2d+14)) .or. (.not. (y <= 2.6d+31))) 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 <= -4.2e+14) || !(y <= 2.6e+31)) {
		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 <= -4.2e+14) or not (y <= 2.6e+31):
		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 <= -4.2e+14) || !(y <= 2.6e+31))
		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 <= -4.2e+14) || ~((y <= 2.6e+31)))
		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, -4.2e+14], N[Not[LessEqual[y, 2.6e+31]], $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 < -4.2e14 or 2.6e31 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in a around 0 95.4%

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

   3. Taylor expanded in t around 0 77.0%

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

   if -4.2e14 < y < 2.6e31

   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 78.7%

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

      1. mul-1-neg 78.7%

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

      2. *-commutative 78.7%

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

      3. distribute-rgt-neg-in 78.7%

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

   4. Simplified 78.7%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+14} \lor \neg \left(y \leq 2.6 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 9: 54.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -70000:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -70000.0) (* x (- 1.0 (* y t))) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -70000.0) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-70000.0d0)) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -70000.0) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -70000.0:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -70000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -70000.0)
		tmp = x * (1.0 - (y * t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -70000.0], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7e4

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 74.0%

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

   3. Taylor expanded in t around inf 74.0%

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

      1. neg-mul-1 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in t around 0 33.8%

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

      1. +-commutative 33.8%

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

      2. mul-1-neg 33.8%

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

      3. *-commutative 33.8%

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

      4. unsub-neg 33.8%

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

      5. *-commutative 33.8%

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

   8. Simplified 33.8%

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

   if -7e4 < t

   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 a around 0 72.0%

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

   3. Taylor expanded in t around 0 65.0%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -70000:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 10: 33.2% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot b\right)\\ t_2 := x + t_1\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{x \cdot x}{t_2}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-55}:\\ \;\;\;\;x - t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot x - t_1 \cdot t_1}{t_2}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+176}:\\ \;\;\;\;\frac{\left(a \cdot a\right) \cdot \left(\left(b \cdot b\right) \cdot \left(x \cdot \left(-x\right)\right)\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* x b))) (t_2 (+ x t_1)))
   (if (<= y -6.2e-93)
     (/ (* x x) t_2)
     (if (<= y 1.52e-55)
       (- x t_1)
       (if (<= y 7.5e+14)
         (/ (- (* x x) (* t_1 t_1)) t_2)
         (if (<= y 9.5e+176)
           (/ (* (* a a) (* (* b b) (* x (- x)))) t_2)
           (- (* y (* x t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (x * b);
	double t_2 = x + t_1;
	double tmp;
	if (y <= -6.2e-93) {
		tmp = (x * x) / t_2;
	} else if (y <= 1.52e-55) {
		tmp = x - t_1;
	} else if (y <= 7.5e+14) {
		tmp = ((x * x) - (t_1 * t_1)) / t_2;
	} else if (y <= 9.5e+176) {
		tmp = ((a * a) * ((b * b) * (x * -x))) / t_2;
	} else {
		tmp = -(y * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (x * b)
    t_2 = x + t_1
    if (y <= (-6.2d-93)) then
        tmp = (x * x) / t_2
    else if (y <= 1.52d-55) then
        tmp = x - t_1
    else if (y <= 7.5d+14) then
        tmp = ((x * x) - (t_1 * t_1)) / t_2
    else if (y <= 9.5d+176) then
        tmp = ((a * a) * ((b * b) * (x * -x))) / t_2
    else
        tmp = -(y * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (x * b);
	double t_2 = x + t_1;
	double tmp;
	if (y <= -6.2e-93) {
		tmp = (x * x) / t_2;
	} else if (y <= 1.52e-55) {
		tmp = x - t_1;
	} else if (y <= 7.5e+14) {
		tmp = ((x * x) - (t_1 * t_1)) / t_2;
	} else if (y <= 9.5e+176) {
		tmp = ((a * a) * ((b * b) * (x * -x))) / t_2;
	} else {
		tmp = -(y * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (x * b)
	t_2 = x + t_1
	tmp = 0
	if y <= -6.2e-93:
		tmp = (x * x) / t_2
	elif y <= 1.52e-55:
		tmp = x - t_1
	elif y <= 7.5e+14:
		tmp = ((x * x) - (t_1 * t_1)) / t_2
	elif y <= 9.5e+176:
		tmp = ((a * a) * ((b * b) * (x * -x))) / t_2
	else:
		tmp = -(y * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(x * b))
	t_2 = Float64(x + t_1)
	tmp = 0.0
	if (y <= -6.2e-93)
		tmp = Float64(Float64(x * x) / t_2);
	elseif (y <= 1.52e-55)
		tmp = Float64(x - t_1);
	elseif (y <= 7.5e+14)
		tmp = Float64(Float64(Float64(x * x) - Float64(t_1 * t_1)) / t_2);
	elseif (y <= 9.5e+176)
		tmp = Float64(Float64(Float64(a * a) * Float64(Float64(b * b) * Float64(x * Float64(-x)))) / t_2);
	else
		tmp = Float64(-Float64(y * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (x * b);
	t_2 = x + t_1;
	tmp = 0.0;
	if (y <= -6.2e-93)
		tmp = (x * x) / t_2;
	elseif (y <= 1.52e-55)
		tmp = x - t_1;
	elseif (y <= 7.5e+14)
		tmp = ((x * x) - (t_1 * t_1)) / t_2;
	elseif (y <= 9.5e+176)
		tmp = ((a * a) * ((b * b) * (x * -x))) / t_2;
	else
		tmp = -(y * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + t$95$1), $MachinePrecision]}, If[LessEqual[y, -6.2e-93], N[(N[(x * x), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 1.52e-55], N[(x - t$95$1), $MachinePrecision], If[LessEqual[y, 7.5e+14], N[(N[(N[(x * x), $MachinePrecision] - N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 9.5e+176], N[(N[(N[(a * a), $MachinePrecision] * N[(N[(b * b), $MachinePrecision] * N[(x * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], (-N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision])]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.19999999999999999e-93

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 44.2%

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

      1. mul-1-neg 44.2%

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

      2. *-commutative 44.2%

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

      3. distribute-rgt-neg-in 44.2%

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

   4. Simplified 44.2%

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

   5. Taylor expanded in b around 0 11.1%

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

      1. +-commutative 11.1%

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

      2. mul-1-neg 11.1%

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

      3. unsub-neg 11.1%

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

   7. Simplified 11.1%

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

      1. cancel-sign-sub-inv 11.1%

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

      2. flip-+ 25.2%

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

   9. Applied egg-rr 25.2%

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

   10. Taylor expanded in a around 0 33.1%

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

       1. unpow2 33.1%

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

   12. Simplified 33.1%

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

   if -6.19999999999999999e-93 < y < 1.5200000000000001e-55

   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 86.3%

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

      1. mul-1-neg 86.3%

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

      2. *-commutative 86.3%

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

      3. distribute-rgt-neg-in 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in b around 0 47.7%

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

      1. +-commutative 47.7%

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

      2. mul-1-neg 47.7%

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

      3. unsub-neg 47.7%

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

   7. Simplified 47.7%

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

   if 1.5200000000000001e-55 < y < 7.5e14

   1. Initial program 94.3%

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

   2. Taylor expanded in b around inf 59.7%

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

      1. mul-1-neg 59.7%

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

      2. *-commutative 59.7%

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

      3. distribute-rgt-neg-in 59.7%

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

   4. Simplified 59.7%

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

   5. Taylor expanded in b around 0 25.3%

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

      1. +-commutative 25.3%

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

      2. mul-1-neg 25.3%

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

      3. unsub-neg 25.3%

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

   7. Simplified 25.3%

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

      1. cancel-sign-sub-inv 25.3%

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

      2. flip-+ 57.6%

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

   9. Applied egg-rr 57.6%

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

   if 7.5e14 < y < 9.4999999999999995e176

   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 42.2%

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

      1. mul-1-neg 42.2%

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

      2. *-commutative 42.2%

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

      3. distribute-rgt-neg-in 42.2%

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

   4. Simplified 42.2%

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

   5. Taylor expanded in b around 0 3.4%

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

      1. +-commutative 3.4%

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

      2. mul-1-neg 3.4%

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

      3. unsub-neg 3.4%

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

   7. Simplified 3.4%

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

      1. cancel-sign-sub-inv 3.4%

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

      2. flip-+ 25.2%

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

   9. Applied egg-rr 25.2%

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

   10. Taylor expanded in a around inf 40.7%

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

       1. mul-1-neg 40.7%

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

       2. unpow2 40.7%

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

       3. unpow2 40.7%

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

       4. unpow2 40.7%

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

   12. Simplified 40.7%

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

   if 9.4999999999999995e176 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 100.0%

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

   3. Taylor expanded in t around inf 54.7%

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

      1. neg-mul-1 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in t around 0 25.0%

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

      1. +-commutative 25.0%

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

      2. mul-1-neg 25.0%

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

      3. *-commutative 25.0%

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

      4. unsub-neg 25.0%

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

      5. *-commutative 25.0%

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

   8. Simplified 25.0%

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

   9. Taylor expanded in y around inf 40.5%

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

       1. mul-1-neg 40.5%

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

   11. Simplified 40.5%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{x \cdot x}{x + a \cdot \left(x \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-55}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot x - \left(a \cdot \left(x \cdot b\right)\right) \cdot \left(a \cdot \left(x \cdot b\right)\right)}{x + a \cdot \left(x \cdot b\right)}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+176}:\\ \;\;\;\;\frac{\left(a \cdot a\right) \cdot \left(\left(b \cdot b\right) \cdot \left(x \cdot \left(-x\right)\right)\right)}{x + a \cdot \left(x \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 11: 33.7% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(x \cdot b\right)\\ t_2 := \frac{x \cdot x}{t_1}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-80}:\\ \;\;\;\;x - a \cdot \left(x \cdot \left(z + b\right)\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+177}:\\ \;\;\;\;\frac{\left(a \cdot a\right) \cdot \left(\left(b \cdot b\right) \cdot \left(x \cdot \left(-x\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (* x b)))) (t_2 (/ (* x x) t_1)))
   (if (<= y -1.05e-102)
     t_2
     (if (<= y 3.2e-80)
       (- x (* a (* x (+ z b))))
       (if (<= y 2.9e+19)
         t_2
         (if (<= y 4.8e+177)
           (/ (* (* a a) (* (* b b) (* x (- x)))) t_1)
           (- (* y (* x t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (x * b));
	double t_2 = (x * x) / t_1;
	double tmp;
	if (y <= -1.05e-102) {
		tmp = t_2;
	} else if (y <= 3.2e-80) {
		tmp = x - (a * (x * (z + b)));
	} else if (y <= 2.9e+19) {
		tmp = t_2;
	} else if (y <= 4.8e+177) {
		tmp = ((a * a) * ((b * b) * (x * -x))) / t_1;
	} else {
		tmp = -(y * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (x * b))
    t_2 = (x * x) / t_1
    if (y <= (-1.05d-102)) then
        tmp = t_2
    else if (y <= 3.2d-80) then
        tmp = x - (a * (x * (z + b)))
    else if (y <= 2.9d+19) then
        tmp = t_2
    else if (y <= 4.8d+177) then
        tmp = ((a * a) * ((b * b) * (x * -x))) / t_1
    else
        tmp = -(y * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (x * b));
	double t_2 = (x * x) / t_1;
	double tmp;
	if (y <= -1.05e-102) {
		tmp = t_2;
	} else if (y <= 3.2e-80) {
		tmp = x - (a * (x * (z + b)));
	} else if (y <= 2.9e+19) {
		tmp = t_2;
	} else if (y <= 4.8e+177) {
		tmp = ((a * a) * ((b * b) * (x * -x))) / t_1;
	} else {
		tmp = -(y * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (x * b))
	t_2 = (x * x) / t_1
	tmp = 0
	if y <= -1.05e-102:
		tmp = t_2
	elif y <= 3.2e-80:
		tmp = x - (a * (x * (z + b)))
	elif y <= 2.9e+19:
		tmp = t_2
	elif y <= 4.8e+177:
		tmp = ((a * a) * ((b * b) * (x * -x))) / t_1
	else:
		tmp = -(y * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(x * b)))
	t_2 = Float64(Float64(x * x) / t_1)
	tmp = 0.0
	if (y <= -1.05e-102)
		tmp = t_2;
	elseif (y <= 3.2e-80)
		tmp = Float64(x - Float64(a * Float64(x * Float64(z + b))));
	elseif (y <= 2.9e+19)
		tmp = t_2;
	elseif (y <= 4.8e+177)
		tmp = Float64(Float64(Float64(a * a) * Float64(Float64(b * b) * Float64(x * Float64(-x)))) / t_1);
	else
		tmp = Float64(-Float64(y * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (x * b));
	t_2 = (x * x) / t_1;
	tmp = 0.0;
	if (y <= -1.05e-102)
		tmp = t_2;
	elseif (y <= 3.2e-80)
		tmp = x - (a * (x * (z + b)));
	elseif (y <= 2.9e+19)
		tmp = t_2;
	elseif (y <= 4.8e+177)
		tmp = ((a * a) * ((b * b) * (x * -x))) / t_1;
	else
		tmp = -(y * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * x), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[y, -1.05e-102], t$95$2, If[LessEqual[y, 3.2e-80], N[(x - N[(a * N[(x * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+19], t$95$2, If[LessEqual[y, 4.8e+177], N[(N[(N[(a * a), $MachinePrecision] * N[(N[(b * b), $MachinePrecision] * N[(x * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], (-N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision])]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.05e-102 or 3.1999999999999999e-80 < y < 2.9e19

   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 b around inf 49.8%

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

      1. mul-1-neg 49.8%

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

      2. *-commutative 49.8%

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

      3. distribute-rgt-neg-in 49.8%

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

   4. Simplified 49.8%

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

   5. Taylor expanded in b around 0 14.4%

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

      1. +-commutative 14.4%

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

      2. mul-1-neg 14.4%

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

      3. unsub-neg 14.4%

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

   7. Simplified 14.4%

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

      1. cancel-sign-sub-inv 14.4%

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

      2. flip-+ 29.0%

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

   9. Applied egg-rr 29.0%

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

   10. Taylor expanded in a around 0 35.7%

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

       1. unpow2 35.7%

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

   12. Simplified 35.7%

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

   if -1.05e-102 < y < 3.1999999999999999e-80

   1. Initial program 96.6%

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

   2. Taylor expanded in y around 0 89.3%

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

      1. sub-neg 89.3%

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

      2. neg-mul-1 89.3%

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

      3. log1p-def 92.6%

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

      4. neg-mul-1 92.6%

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

   4. Simplified 92.6%

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

   5. Taylor expanded in z around 0 92.6%

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

      1. neg-mul-1 92.6%

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

      2. unsub-neg 92.6%

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

      3. neg-mul-1 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in a around 0 50.1%

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

      1. +-commutative 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

      4. +-commutative 50.1%

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

   10. Simplified 50.1%

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

   if 2.9e19 < y < 4.8e177

   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 41.5%

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

      1. mul-1-neg 41.5%

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

      2. *-commutative 41.5%

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

      3. distribute-rgt-neg-in 41.5%

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

   4. Simplified 41.5%

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

   5. Taylor expanded in b around 0 3.5%

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

      1. +-commutative 3.5%

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

      2. mul-1-neg 3.5%

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

      3. unsub-neg 3.5%

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

   7. Simplified 3.5%

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

      1. cancel-sign-sub-inv 3.5%

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

      2. flip-+ 26.9%

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

   9. Applied egg-rr 26.9%

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

   10. Taylor expanded in a around inf 43.5%

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

       1. mul-1-neg 43.5%

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

       2. unpow2 43.5%

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

       3. unpow2 43.5%

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

       4. unpow2 43.5%

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

   12. Simplified 43.5%

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

   if 4.8e177 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 100.0%

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

   3. Taylor expanded in t around inf 54.7%

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

      1. neg-mul-1 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in t around 0 25.0%

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

      1. +-commutative 25.0%

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

      2. mul-1-neg 25.0%

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

      3. *-commutative 25.0%

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

      4. unsub-neg 25.0%

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

      5. *-commutative 25.0%

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

   8. Simplified 25.0%

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

   9. Taylor expanded in y around inf 40.5%

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

       1. mul-1-neg 40.5%

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

   11. Simplified 40.5%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-102}:\\ \;\;\;\;\frac{x \cdot x}{x + a \cdot \left(x \cdot b\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-80}:\\ \;\;\;\;x - a \cdot \left(x \cdot \left(z + b\right)\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot x}{x + a \cdot \left(x \cdot b\right)}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+177}:\\ \;\;\;\;\frac{\left(a \cdot a\right) \cdot \left(\left(b \cdot b\right) \cdot \left(x \cdot \left(-x\right)\right)\right)}{x + a \cdot \left(x \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 12: 30.8% accurate, 12.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot b\right)\\ t_2 := \frac{x \cdot x}{x + t_1}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-179}:\\ \;\;\;\;x - t_1\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-10}:\\ \;\;\;\;\frac{1 - \left(a \cdot a\right) \cdot \left(b \cdot b\right)}{\frac{a \cdot b + 1}{x}}\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* x b))) (t_2 (/ (* x x) (+ x t_1))))
   (if (<= y -4.6e-93)
     t_2
     (if (<= y -8.4e-179)
       (- x t_1)
       (if (<= y -3.6e-228)
         t_2
         (if (<= y 1.6e-10)
           (/ (- 1.0 (* (* a a) (* b b))) (/ (+ (* a b) 1.0) x))
           (- (* y (* x t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (x * b);
	double t_2 = (x * x) / (x + t_1);
	double tmp;
	if (y <= -4.6e-93) {
		tmp = t_2;
	} else if (y <= -8.4e-179) {
		tmp = x - t_1;
	} else if (y <= -3.6e-228) {
		tmp = t_2;
	} else if (y <= 1.6e-10) {
		tmp = (1.0 - ((a * a) * (b * b))) / (((a * b) + 1.0) / x);
	} else {
		tmp = -(y * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (x * b)
    t_2 = (x * x) / (x + t_1)
    if (y <= (-4.6d-93)) then
        tmp = t_2
    else if (y <= (-8.4d-179)) then
        tmp = x - t_1
    else if (y <= (-3.6d-228)) then
        tmp = t_2
    else if (y <= 1.6d-10) then
        tmp = (1.0d0 - ((a * a) * (b * b))) / (((a * b) + 1.0d0) / x)
    else
        tmp = -(y * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (x * b);
	double t_2 = (x * x) / (x + t_1);
	double tmp;
	if (y <= -4.6e-93) {
		tmp = t_2;
	} else if (y <= -8.4e-179) {
		tmp = x - t_1;
	} else if (y <= -3.6e-228) {
		tmp = t_2;
	} else if (y <= 1.6e-10) {
		tmp = (1.0 - ((a * a) * (b * b))) / (((a * b) + 1.0) / x);
	} else {
		tmp = -(y * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (x * b)
	t_2 = (x * x) / (x + t_1)
	tmp = 0
	if y <= -4.6e-93:
		tmp = t_2
	elif y <= -8.4e-179:
		tmp = x - t_1
	elif y <= -3.6e-228:
		tmp = t_2
	elif y <= 1.6e-10:
		tmp = (1.0 - ((a * a) * (b * b))) / (((a * b) + 1.0) / x)
	else:
		tmp = -(y * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(x * b))
	t_2 = Float64(Float64(x * x) / Float64(x + t_1))
	tmp = 0.0
	if (y <= -4.6e-93)
		tmp = t_2;
	elseif (y <= -8.4e-179)
		tmp = Float64(x - t_1);
	elseif (y <= -3.6e-228)
		tmp = t_2;
	elseif (y <= 1.6e-10)
		tmp = Float64(Float64(1.0 - Float64(Float64(a * a) * Float64(b * b))) / Float64(Float64(Float64(a * b) + 1.0) / x));
	else
		tmp = Float64(-Float64(y * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (x * b);
	t_2 = (x * x) / (x + t_1);
	tmp = 0.0;
	if (y <= -4.6e-93)
		tmp = t_2;
	elseif (y <= -8.4e-179)
		tmp = x - t_1;
	elseif (y <= -3.6e-228)
		tmp = t_2;
	elseif (y <= 1.6e-10)
		tmp = (1.0 - ((a * a) * (b * b))) / (((a * b) + 1.0) / x);
	else
		tmp = -(y * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * x), $MachinePrecision] / N[(x + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e-93], t$95$2, If[LessEqual[y, -8.4e-179], N[(x - t$95$1), $MachinePrecision], If[LessEqual[y, -3.6e-228], t$95$2, If[LessEqual[y, 1.6e-10], N[(N[(1.0 - N[(N[(a * a), $MachinePrecision] * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(a * b), $MachinePrecision] + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], (-N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision])]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.5999999999999996e-93 or -8.3999999999999995e-179 < y < -3.6000000000000002e-228

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 48.9%

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

      1. mul-1-neg 48.9%

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

      2. *-commutative 48.9%

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

      3. distribute-rgt-neg-in 48.9%

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

   4. Simplified 48.9%

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

   5. Taylor expanded in b around 0 15.0%

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

      1. +-commutative 15.0%

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

      2. mul-1-neg 15.0%

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

      3. unsub-neg 15.0%

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

   7. Simplified 15.0%

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

      1. cancel-sign-sub-inv 15.0%

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

      2. flip-+ 26.7%

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

   9. Applied egg-rr 26.7%

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

   10. Taylor expanded in a around 0 37.5%

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

       1. unpow2 37.5%

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

   12. Simplified 37.5%

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

   if -4.5999999999999996e-93 < y < -8.3999999999999995e-179

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 82.2%

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

      1. mul-1-neg 82.2%

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

      2. *-commutative 82.2%

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

      3. distribute-rgt-neg-in 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in b around 0 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

   7. Simplified 58.3%

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

   if -3.6000000000000002e-228 < y < 1.5999999999999999e-10

   1. Initial program 95.3%

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

   2. Taylor expanded in b around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. *-commutative 86.0%

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

      3. distribute-rgt-neg-in 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in b around 0 44.5%

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

      1. +-commutative 44.5%

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

      2. mul-1-neg 44.5%

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

      3. unsub-neg 44.5%

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

   7. Simplified 44.5%

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

      1. cancel-sign-sub-inv 44.5%

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

      2. flip-+ 33.8%

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

   9. Applied egg-rr 33.8%

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

   10. Taylor expanded in x around 0 51.6%

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

       1. neg-mul-1 51.6%

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

       2. distribute-lft-neg-in 51.6%

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

       3. cancel-sign-sub 51.6%

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

       4. +-commutative 51.6%

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

       5. associate-/l* 47.8%

          \[\leadsto \color{blue}{\frac{1 - {a}^{2} \cdot {b}^{2}}{\frac{a \cdot b + 1}{x}}} \]

       6. unpow2 47.8%

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

       7. unpow2 47.8%

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

       8. +-commutative 47.8%

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

       9. cancel-sign-sub 47.8%

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

   12. Simplified 47.8%

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

   if 1.5999999999999999e-10 < 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 a around 0 90.7%

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

   3. Taylor expanded in t around inf 46.5%

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

      1. neg-mul-1 46.5%

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

   5. Simplified 46.5%

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

   6. Taylor expanded in t around 0 20.3%

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

      1. +-commutative 20.3%

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

      2. mul-1-neg 20.3%

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

      3. *-commutative 20.3%

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

      4. unsub-neg 20.3%

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

      5. *-commutative 20.3%

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

   8. Simplified 20.3%

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

   9. Taylor expanded in y around inf 31.7%

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

       1. mul-1-neg 31.7%

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

   11. Simplified 31.7%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{x \cdot x}{x + a \cdot \left(x \cdot b\right)}\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-179}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-228}:\\ \;\;\;\;\frac{x \cdot x}{x + a \cdot \left(x \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-10}:\\ \;\;\;\;\frac{1 - \left(a \cdot a\right) \cdot \left(b \cdot b\right)}{\frac{a \cdot b + 1}{x}}\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 13: 33.8% accurate, 20.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-93} \lor \neg \left(y \leq 2 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{x \cdot x}{x + a \cdot \left(x \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot \left(z + b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.3e-93) (not (<= y 2e-80)))
   (/ (* x x) (+ x (* a (* x b))))
   (- x (* a (* x (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e-93) || !(y <= 2e-80)) {
		tmp = (x * x) / (x + (a * (x * b)));
	} else {
		tmp = x - (a * (x * (z + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.3d-93)) .or. (.not. (y <= 2d-80))) then
        tmp = (x * x) / (x + (a * (x * b)))
    else
        tmp = x - (a * (x * (z + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e-93) || !(y <= 2e-80)) {
		tmp = (x * x) / (x + (a * (x * b)));
	} else {
		tmp = x - (a * (x * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.3e-93) or not (y <= 2e-80):
		tmp = (x * x) / (x + (a * (x * b)))
	else:
		tmp = x - (a * (x * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.3e-93) || !(y <= 2e-80))
		tmp = Float64(Float64(x * x) / Float64(x + Float64(a * Float64(x * b))));
	else
		tmp = Float64(x - Float64(a * Float64(x * Float64(z + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.3e-93) || ~((y <= 2e-80)))
		tmp = (x * x) / (x + (a * (x * b)));
	else
		tmp = x - (a * (x * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.3e-93], N[Not[LessEqual[y, 2e-80]], $MachinePrecision]], N[(N[(x * x), $MachinePrecision] / N[(x + N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(x * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999998e-93 or 1.99999999999999992e-80 < y

   1. Initial program 98.2%

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

   2. Taylor expanded in b around inf 44.3%

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

      1. mul-1-neg 44.3%

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

      2. *-commutative 44.3%

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

      3. distribute-rgt-neg-in 44.3%

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

   4. Simplified 44.3%

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

   5. Taylor expanded in b around 0 10.3%

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

      1. +-commutative 10.3%

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

      2. mul-1-neg 10.3%

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

      3. unsub-neg 10.3%

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

   7. Simplified 10.3%

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

      1. cancel-sign-sub-inv 10.3%

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

      2. flip-+ 28.7%

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

   9. Applied egg-rr 28.7%

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

   10. Taylor expanded in a around 0 33.0%

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

       1. unpow2 33.0%

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

   12. Simplified 33.0%

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

   if -2.2999999999999998e-93 < y < 1.99999999999999992e-80

   1. Initial program 96.6%

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

   2. Taylor expanded in y around 0 89.3%

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

      1. sub-neg 89.3%

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

      2. neg-mul-1 89.3%

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

      3. log1p-def 92.6%

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

      4. neg-mul-1 92.6%

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

   4. Simplified 92.6%

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

   5. Taylor expanded in z around 0 92.6%

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

      1. neg-mul-1 92.6%

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

      2. unsub-neg 92.6%

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

      3. neg-mul-1 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in a around 0 50.1%

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

      1. +-commutative 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

      4. +-commutative 50.1%

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

   10. Simplified 50.1%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-93} \lor \neg \left(y \leq 2 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{x \cdot x}{x + a \cdot \left(x \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot \left(z + b\right)\right)\\ \end{array} \]

Alternative 14: 31.2% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-12}:\\ \;\;\;\;x - a \cdot \left(x \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.6e-33)
   (* a (* x (- b)))
   (if (<= y 1.1e-12) (- x (* a (* x (+ z b)))) (- (* y (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e-33) {
		tmp = a * (x * -b);
	} else if (y <= 1.1e-12) {
		tmp = x - (a * (x * (z + b)));
	} else {
		tmp = -(y * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.6d-33)) then
        tmp = a * (x * -b)
    else if (y <= 1.1d-12) then
        tmp = x - (a * (x * (z + b)))
    else
        tmp = -(y * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e-33) {
		tmp = a * (x * -b);
	} else if (y <= 1.1e-12) {
		tmp = x - (a * (x * (z + b)));
	} else {
		tmp = -(y * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.6e-33:
		tmp = a * (x * -b)
	elif y <= 1.1e-12:
		tmp = x - (a * (x * (z + b)))
	else:
		tmp = -(y * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.6e-33)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= 1.1e-12)
		tmp = Float64(x - Float64(a * Float64(x * Float64(z + b))));
	else
		tmp = Float64(-Float64(y * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.6e-33)
		tmp = a * (x * -b);
	elseif (y <= 1.1e-12)
		tmp = x - (a * (x * (z + b)));
	else
		tmp = -(y * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.6e-33], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-12], N[(x - N[(a * N[(x * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999988e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 36.2%

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

      1. mul-1-neg 36.2%

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

      2. *-commutative 36.2%

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

      3. distribute-rgt-neg-in 36.2%

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

   4. Simplified 36.2%

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

   5. Taylor expanded in b around 0 8.2%

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

      1. +-commutative 8.2%

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

      2. mul-1-neg 8.2%

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

      3. unsub-neg 8.2%

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

   7. Simplified 8.2%

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

   8. Taylor expanded in a around inf 19.6%

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

      1. neg-mul-1 19.6%

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

      2. distribute-rgt-neg-in 19.6%

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

      3. distribute-rgt-neg-in 19.6%

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

   10. Simplified 19.6%

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

   if -1.59999999999999988e-33 < y < 1.09999999999999996e-12

   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 y around 0 88.0%

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

      1. sub-neg 88.0%

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

      2. neg-mul-1 88.0%

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

      3. log1p-def 91.3%

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

      4. neg-mul-1 91.3%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in z around 0 91.3%

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

      1. neg-mul-1 91.3%

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

      2. unsub-neg 91.3%

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

      3. neg-mul-1 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in a around 0 44.6%

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

      1. +-commutative 44.6%

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

      2. mul-1-neg 44.6%

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

      3. unsub-neg 44.6%

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

      4. +-commutative 44.6%

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

   10. Simplified 44.6%

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

   if 1.09999999999999996e-12 < 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 a around 0 90.7%

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

   3. Taylor expanded in t around inf 46.5%

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

      1. neg-mul-1 46.5%

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

   5. Simplified 46.5%

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

   6. Taylor expanded in t around 0 20.3%

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

      1. +-commutative 20.3%

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

      2. mul-1-neg 20.3%

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

      3. *-commutative 20.3%

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

      4. unsub-neg 20.3%

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

      5. *-commutative 20.3%

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

   8. Simplified 20.3%

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

   9. Taylor expanded in y around inf 31.7%

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

       1. mul-1-neg 31.7%

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

   11. Simplified 31.7%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-12}:\\ \;\;\;\;x - a \cdot \left(x \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 15: 29.4% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(-y \cdot t\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.5e+159)
   (* x (- (* y t)))
   (if (<= a 3.8e-33) (* x (- 1.0 (* y t))) (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.5e+159) {
		tmp = x * -(y * t);
	} else if (a <= 3.8e-33) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = a * (x * -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 (a <= (-1.5d+159)) then
        tmp = x * -(y * t)
    else if (a <= 3.8d-33) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = a * (x * -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 (a <= -1.5e+159) {
		tmp = x * -(y * t);
	} else if (a <= 3.8e-33) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.5e+159:
		tmp = x * -(y * t)
	elif a <= 3.8e-33:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.5e+159)
		tmp = Float64(x * Float64(-Float64(y * t)));
	elseif (a <= 3.8e-33)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.5e+159)
		tmp = x * -(y * t);
	elseif (a <= 3.8e-33)
		tmp = x * (1.0 - (y * t));
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.5e+159], N[(x * (-N[(y * t), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, 3.8e-33], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5000000000000001e159

   1. Initial program 91.4%

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

   2. Taylor expanded in a around 0 28.1%

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

   3. Taylor expanded in t around inf 15.9%

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

      1. neg-mul-1 15.9%

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

   5. Simplified 15.9%

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

   6. Taylor expanded in t around 0 2.9%

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

      1. +-commutative 2.9%

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

      2. mul-1-neg 2.9%

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

      3. *-commutative 2.9%

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

      4. unsub-neg 2.9%

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

      5. *-commutative 2.9%

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

   8. Simplified 2.9%

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

   9. Taylor expanded in y around inf 19.3%

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

       1. mul-1-neg 19.3%

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

       2. associate-*r* 31.6%

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

       3. distribute-rgt-neg-in 31.6%

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

   11. Simplified 31.6%

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

   if -1.5000000000000001e159 < a < 3.79999999999999994e-33

   1. Initial program 99.4%

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

   2. Taylor expanded in a around 0 85.6%

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

   3. Taylor expanded in t around inf 62.3%

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

      1. neg-mul-1 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in t around 0 39.7%

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

      1. +-commutative 39.7%

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

      2. mul-1-neg 39.7%

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

      3. *-commutative 39.7%

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

      4. unsub-neg 39.7%

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

      5. *-commutative 39.7%

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

   8. Simplified 39.7%

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

   if 3.79999999999999994e-33 < a

   1. Initial program 95.8%

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

   2. Taylor expanded in b around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. *-commutative 67.2%

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

      3. distribute-rgt-neg-in 67.2%

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

   4. Simplified 67.2%

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

   5. Taylor expanded in b around 0 14.0%

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

      1. +-commutative 14.0%

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

      2. mul-1-neg 14.0%

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

      3. 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 23.6%

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

      1. neg-mul-1 23.6%

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

      2. distribute-rgt-neg-in 23.6%

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

      3. distribute-rgt-neg-in 23.6%

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

   10. Simplified 23.6%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(-y \cdot t\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 16: 30.8% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-13}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.7e-33)
   (* a (* x (- b)))
   (if (<= y 5.2e-13) (- x (* a (* x b))) (- (* y (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e-33) {
		tmp = a * (x * -b);
	} else if (y <= 5.2e-13) {
		tmp = x - (a * (x * b));
	} else {
		tmp = -(y * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.7d-33)) then
        tmp = a * (x * -b)
    else if (y <= 5.2d-13) then
        tmp = x - (a * (x * b))
    else
        tmp = -(y * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e-33) {
		tmp = a * (x * -b);
	} else if (y <= 5.2e-13) {
		tmp = x - (a * (x * b));
	} else {
		tmp = -(y * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.7e-33:
		tmp = a * (x * -b)
	elif y <= 5.2e-13:
		tmp = x - (a * (x * b))
	else:
		tmp = -(y * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.7e-33)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= 5.2e-13)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	else
		tmp = Float64(-Float64(y * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.7e-33)
		tmp = a * (x * -b);
	elseif (y <= 5.2e-13)
		tmp = x - (a * (x * b));
	else
		tmp = -(y * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.7e-33], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-13], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 36.2%

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

      1. mul-1-neg 36.2%

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

      2. *-commutative 36.2%

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

      3. distribute-rgt-neg-in 36.2%

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

   4. Simplified 36.2%

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

   5. Taylor expanded in b around 0 8.2%

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

      1. +-commutative 8.2%

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

      2. mul-1-neg 8.2%

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

      3. unsub-neg 8.2%

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

   7. Simplified 8.2%

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

   8. Taylor expanded in a around inf 19.6%

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

      1. neg-mul-1 19.6%

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

      2. distribute-rgt-neg-in 19.6%

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

      3. distribute-rgt-neg-in 19.6%

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

   10. Simplified 19.6%

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

   if -1.7e-33 < y < 5.2000000000000001e-13

   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 85.6%

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

      1. mul-1-neg 85.6%

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

      2. *-commutative 85.6%

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

      3. distribute-rgt-neg-in 85.6%

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

   4. Simplified 85.6%

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

   5. Taylor expanded in b around 0 44.6%

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

      1. +-commutative 44.6%

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

      2. mul-1-neg 44.6%

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

      3. unsub-neg 44.6%

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

   7. Simplified 44.6%

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

   if 5.2000000000000001e-13 < 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 a around 0 90.7%

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

   3. Taylor expanded in t around inf 46.5%

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

      1. neg-mul-1 46.5%

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

   5. Simplified 46.5%

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

   6. Taylor expanded in t around 0 20.3%

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

      1. +-commutative 20.3%

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

      2. mul-1-neg 20.3%

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

      3. *-commutative 20.3%

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

      4. unsub-neg 20.3%

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

      5. *-commutative 20.3%

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

   8. Simplified 20.3%

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

   9. Taylor expanded in y around inf 31.7%

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

       1. mul-1-neg 31.7%

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

   11. Simplified 31.7%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-13}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 17: 26.8% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-62} \lor \neg \left(y \leq 6.5 \cdot 10^{-11}\right):\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.55e-62) (not (<= y 6.5e-11))) (- (* y (* x t))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.55e-62) || !(y <= 6.5e-11)) {
		tmp = -(y * (x * t));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.55d-62)) .or. (.not. (y <= 6.5d-11))) then
        tmp = -(y * (x * t))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.55e-62) || !(y <= 6.5e-11)) {
		tmp = -(y * (x * t));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.55e-62) or not (y <= 6.5e-11):
		tmp = -(y * (x * t))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.55e-62) || !(y <= 6.5e-11))
		tmp = Float64(-Float64(y * Float64(x * t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.55e-62) || ~((y <= 6.5e-11)))
		tmp = -(y * (x * t));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.55e-62], N[Not[LessEqual[y, 6.5e-11]], $MachinePrecision]], (-N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), x]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e-62 or 6.49999999999999953e-11 < y

   1. Initial program 98.6%

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

   2. Taylor expanded in a around 0 88.8%

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

   3. Taylor expanded in t around inf 52.8%

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

      1. neg-mul-1 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in t around 0 17.1%

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

      1. +-commutative 17.1%

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

      2. mul-1-neg 17.1%

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

      3. *-commutative 17.1%

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

      4. unsub-neg 17.1%

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

      5. *-commutative 17.1%

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

   8. Simplified 17.1%

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

   9. Taylor expanded in y around inf 23.1%

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

       1. mul-1-neg 23.1%

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

   11. Simplified 23.1%

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

   if -1.55e-62 < y < 6.49999999999999953e-11

   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 86.5%

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

      1. mul-1-neg 86.5%

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

      2. *-commutative 86.5%

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

      3. distribute-rgt-neg-in 86.5%

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

   4. Simplified 86.5%

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

   5. Taylor expanded in b around 0 40.7%

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

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-62} \lor \neg \left(y \leq 6.5 \cdot 10^{-11}\right):\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 27.1% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.7e-33)
   (* a (* x (- b)))
   (if (<= y 2.2e-10) x (- (* y (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e-33) {
		tmp = a * (x * -b);
	} else if (y <= 2.2e-10) {
		tmp = x;
	} else {
		tmp = -(y * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.7d-33)) then
        tmp = a * (x * -b)
    else if (y <= 2.2d-10) then
        tmp = x
    else
        tmp = -(y * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e-33) {
		tmp = a * (x * -b);
	} else if (y <= 2.2e-10) {
		tmp = x;
	} else {
		tmp = -(y * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.7e-33:
		tmp = a * (x * -b)
	elif y <= 2.2e-10:
		tmp = x
	else:
		tmp = -(y * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.7e-33)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= 2.2e-10)
		tmp = x;
	else
		tmp = Float64(-Float64(y * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.7e-33)
		tmp = a * (x * -b);
	elseif (y <= 2.2e-10)
		tmp = x;
	else
		tmp = -(y * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.7e-33], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e-10], x, (-N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 36.2%

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

      1. mul-1-neg 36.2%

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

      2. *-commutative 36.2%

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

      3. distribute-rgt-neg-in 36.2%

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

   4. Simplified 36.2%

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

   5. Taylor expanded in b around 0 8.2%

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

      1. +-commutative 8.2%

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

      2. mul-1-neg 8.2%

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

      3. unsub-neg 8.2%

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

   7. Simplified 8.2%

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

   8. Taylor expanded in a around inf 19.6%

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

      1. neg-mul-1 19.6%

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

      2. distribute-rgt-neg-in 19.6%

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

      3. distribute-rgt-neg-in 19.6%

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

   10. Simplified 19.6%

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

   if -1.7e-33 < y < 2.1999999999999999e-10

   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 85.6%

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

      1. mul-1-neg 85.6%

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

      2. *-commutative 85.6%

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

      3. distribute-rgt-neg-in 85.6%

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

   4. Simplified 85.6%

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

   5. Taylor expanded in b around 0 39.4%

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

   if 2.1999999999999999e-10 < 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 a around 0 90.7%

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

   3. Taylor expanded in t around inf 46.5%

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

      1. neg-mul-1 46.5%

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

   5. Simplified 46.5%

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

   6. Taylor expanded in t around 0 20.3%

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

      1. +-commutative 20.3%

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

      2. mul-1-neg 20.3%

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

      3. *-commutative 20.3%

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

      4. unsub-neg 20.3%

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

      5. *-commutative 20.3%

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

   8. Simplified 20.3%

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

   9. Taylor expanded in y around inf 31.7%

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

       1. mul-1-neg 31.7%

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

   11. Simplified 31.7%

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

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 19: 19.4% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 b around inf 59.0%

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

   1. mul-1-neg 59.0%

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

   2. *-commutative 59.0%

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

   3. distribute-rgt-neg-in 59.0%

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

4. Simplified 59.0%

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

5. Taylor expanded in b around 0 20.5%

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

6. Final simplification 20.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023199 
(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))))))