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

Percentage Accurate: 96.4% → 99.5%

Time: 18.5s

Alternatives: 17

Speedup: 1.0×

• 20.8% 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: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

   1. +-commutative 94.8%

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

   2. fma-def 95.2%

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

   3. sub-neg 95.2%

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

   4. log1p-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

2. Final simplification 94.8%

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

Alternative 3: 87.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -960 \lor \neg \left(y \leq 2.8 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -960.0) (not (<= y 2.8e-5)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (log1p (- z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -960.0) || !(y <= 2.8e-5)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * (log1p(-z) - b)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -960.0) || !(y <= 2.8e-5)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * (Math.log1p(-z) - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -960.0) or not (y <= 2.8e-5):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * (math.log1p(-z) - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -960.0) || !(y <= 2.8e-5))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(log1p(Float64(-z)) - b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -960.0], N[Not[LessEqual[y, 2.8e-5]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[(N[Log[1 + (-z)], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -960 or 2.79999999999999996e-5 < y

   1. Initial program 97.7%

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

   2. Taylor expanded in y around inf 91.6%

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

   if -960 < y < 2.79999999999999996e-5

   1. Initial program 91.9%

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

   2. Taylor expanded in y around 0 81.9%

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

      1. sub-neg 81.9%

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

      2. neg-mul-1 81.9%

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

      3. log1p-def 89.9%

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

      4. neg-mul-1 89.9%

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

   4. Simplified 89.9%

      \[\leadsto x \cdot e^{\color{blue}{\left(\mathsf{log1p}\left(-z\right) - b\right) \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -960 \lor \neg \left(y \leq 2.8 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}\\ \end{array} \]

Alternative 4: 87.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -960 \lor \neg \left(y \leq 1.45 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -960.0) (not (<= y 1.45e-5)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (- z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -960.0) || !(y <= 1.45e-5)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * (-z - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-960.0d0)) .or. (.not. (y <= 1.45d-5))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((a * (-z - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -960.0) || !(y <= 1.45e-5)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * (-z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -960.0) or not (y <= 1.45e-5):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * (-z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -960.0) || !(y <= 1.45e-5))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -960.0) || ~((y <= 1.45e-5)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((a * (-z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -960.0], N[Not[LessEqual[y, 1.45e-5]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -960 or 1.45e-5 < y

   1. Initial program 97.7%

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

   2. Taylor expanded in y around inf 91.6%

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

   if -960 < y < 1.45e-5

   1. Initial program 91.9%

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

   2. Taylor expanded in y around 0 81.9%

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

      1. sub-neg 81.9%

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

      2. neg-mul-1 81.9%

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

      3. log1p-def 89.9%

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

      4. neg-mul-1 89.9%

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

   4. Simplified 89.9%

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

   5. Taylor expanded in z around 0 89.7%

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

      1. associate-*r* 89.7%

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

      2. neg-mul-1 89.7%

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

      3. associate-*r* 89.7%

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

      4. neg-mul-1 89.7%

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

      5. distribute-lft-out 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -960 \lor \neg \left(y \leq 1.45 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \]

Alternative 5: 70.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{-y \cdot t}\\ t_2 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7700000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+47}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+79} \lor \neg \left(y \leq 4 \cdot 10^{+132}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (- (* y t))))) (t_2 (* x (pow z y))))
   (if (<= y -2.2e+178)
     t_2
     (if (<= y -7700000000000.0)
       t_1
       (if (<= y 6.8e+47)
         (* x (exp (* a (- b))))
         (if (or (<= y 6.5e+79) (not (<= y 4e+132))) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp(-(y * t));
	double t_2 = x * pow(z, y);
	double tmp;
	if (y <= -2.2e+178) {
		tmp = t_2;
	} else if (y <= -7700000000000.0) {
		tmp = t_1;
	} else if (y <= 6.8e+47) {
		tmp = x * exp((a * -b));
	} else if ((y <= 6.5e+79) || !(y <= 4e+132)) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * exp(-(y * t))
    t_2 = x * (z ** y)
    if (y <= (-2.2d+178)) then
        tmp = t_2
    else if (y <= (-7700000000000.0d0)) then
        tmp = t_1
    else if (y <= 6.8d+47) then
        tmp = x * exp((a * -b))
    else if ((y <= 6.5d+79) .or. (.not. (y <= 4d+132))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp(-(y * t));
	double t_2 = x * Math.pow(z, y);
	double tmp;
	if (y <= -2.2e+178) {
		tmp = t_2;
	} else if (y <= -7700000000000.0) {
		tmp = t_1;
	} else if (y <= 6.8e+47) {
		tmp = x * Math.exp((a * -b));
	} else if ((y <= 6.5e+79) || !(y <= 4e+132)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp(-(y * t))
	t_2 = x * math.pow(z, y)
	tmp = 0
	if y <= -2.2e+178:
		tmp = t_2
	elif y <= -7700000000000.0:
		tmp = t_1
	elif y <= 6.8e+47:
		tmp = x * math.exp((a * -b))
	elif (y <= 6.5e+79) or not (y <= 4e+132):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(-Float64(y * t))))
	t_2 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -2.2e+178)
		tmp = t_2;
	elseif (y <= -7700000000000.0)
		tmp = t_1;
	elseif (y <= 6.8e+47)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif ((y <= 6.5e+79) || !(y <= 4e+132))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp(-(y * t));
	t_2 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -2.2e+178)
		tmp = t_2;
	elseif (y <= -7700000000000.0)
		tmp = t_1;
	elseif (y <= 6.8e+47)
		tmp = x * exp((a * -b));
	elseif ((y <= 6.5e+79) || ~((y <= 4e+132)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[(-N[(y * t), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+178], t$95$2, If[LessEqual[y, -7700000000000.0], t$95$1, If[LessEqual[y, 6.8e+47], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 6.5e+79], N[Not[LessEqual[y, 4e+132]], $MachinePrecision]], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.19999999999999997e178 or 6.7999999999999996e47 < y < 6.49999999999999954e79 or 3.99999999999999996e132 < 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 y around inf 91.8%

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

   3. Taylor expanded in t around 0 83.6%

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

   if -2.19999999999999997e178 < y < -7.7e12 or 6.49999999999999954e79 < y < 3.99999999999999996e132

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf 75.6%

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

      1. mul-1-neg 75.6%

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

      2. distribute-rgt-neg-out 75.6%

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

   4. Simplified 75.6%

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

   if -7.7e12 < y < 6.7999999999999996e47

   1. Initial program 91.9%

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

   2. Taylor expanded in b around inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. *-commutative 79.9%

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

      3. distribute-rgt-neg-in 79.9%

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

   4. Simplified 79.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+178}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq -7700000000000:\\ \;\;\;\;x \cdot e^{-y \cdot t}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+47}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+79} \lor \neg \left(y \leq 4 \cdot 10^{+132}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{-y \cdot t}\\ \end{array} \]

Alternative 6: 73.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{-y \cdot t}\\ t_2 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4150000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+48}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+75} \lor \neg \left(y \leq 5.8 \cdot 10^{+132}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (- (* y t))))) (t_2 (* x (pow z y))))
   (if (<= y -1.9e+175)
     t_2
     (if (<= y -4150000000000.0)
       t_1
       (if (<= y 2.65e+48)
         (* x (exp (* a (- (- z) b))))
         (if (or (<= y 8.2e+75) (not (<= y 5.8e+132))) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp(-(y * t));
	double t_2 = x * pow(z, y);
	double tmp;
	if (y <= -1.9e+175) {
		tmp = t_2;
	} else if (y <= -4150000000000.0) {
		tmp = t_1;
	} else if (y <= 2.65e+48) {
		tmp = x * exp((a * (-z - b)));
	} else if ((y <= 8.2e+75) || !(y <= 5.8e+132)) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * exp(-(y * t))
    t_2 = x * (z ** y)
    if (y <= (-1.9d+175)) then
        tmp = t_2
    else if (y <= (-4150000000000.0d0)) then
        tmp = t_1
    else if (y <= 2.65d+48) then
        tmp = x * exp((a * (-z - b)))
    else if ((y <= 8.2d+75) .or. (.not. (y <= 5.8d+132))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp(-(y * t));
	double t_2 = x * Math.pow(z, y);
	double tmp;
	if (y <= -1.9e+175) {
		tmp = t_2;
	} else if (y <= -4150000000000.0) {
		tmp = t_1;
	} else if (y <= 2.65e+48) {
		tmp = x * Math.exp((a * (-z - b)));
	} else if ((y <= 8.2e+75) || !(y <= 5.8e+132)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp(-(y * t))
	t_2 = x * math.pow(z, y)
	tmp = 0
	if y <= -1.9e+175:
		tmp = t_2
	elif y <= -4150000000000.0:
		tmp = t_1
	elif y <= 2.65e+48:
		tmp = x * math.exp((a * (-z - b)))
	elif (y <= 8.2e+75) or not (y <= 5.8e+132):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(-Float64(y * t))))
	t_2 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -1.9e+175)
		tmp = t_2;
	elseif (y <= -4150000000000.0)
		tmp = t_1;
	elseif (y <= 2.65e+48)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	elseif ((y <= 8.2e+75) || !(y <= 5.8e+132))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp(-(y * t));
	t_2 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -1.9e+175)
		tmp = t_2;
	elseif (y <= -4150000000000.0)
		tmp = t_1;
	elseif (y <= 2.65e+48)
		tmp = x * exp((a * (-z - b)));
	elseif ((y <= 8.2e+75) || ~((y <= 5.8e+132)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[(-N[(y * t), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+175], t$95$2, If[LessEqual[y, -4150000000000.0], t$95$1, If[LessEqual[y, 2.65e+48], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.2e+75], N[Not[LessEqual[y, 5.8e+132]], $MachinePrecision]], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8999999999999998e175 or 2.65e48 < y < 8.1999999999999997e75 or 5.7999999999999997e132 < 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 y around inf 91.8%

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

   3. Taylor expanded in t around 0 83.6%

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

   if -1.8999999999999998e175 < y < -4.15e12 or 8.1999999999999997e75 < y < 5.7999999999999997e132

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf 75.6%

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

      1. mul-1-neg 75.6%

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

      2. distribute-rgt-neg-out 75.6%

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

   4. Simplified 75.6%

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

   if -4.15e12 < y < 2.65e48

   1. Initial program 91.9%

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

   2. Taylor expanded in y around 0 80.1%

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

      1. sub-neg 80.1%

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

      2. neg-mul-1 80.1%

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

      3. log1p-def 88.0%

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

      4. neg-mul-1 88.0%

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

   4. Simplified 88.0%

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

   5. Taylor expanded in z around 0 87.9%

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

      1. associate-*r* 87.9%

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

      2. neg-mul-1 87.9%

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

      3. associate-*r* 87.9%

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

      4. neg-mul-1 87.9%

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

      5. distribute-lft-out 87.9%

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

   7. Simplified 87.9%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+175}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq -4150000000000:\\ \;\;\;\;x \cdot e^{-y \cdot t}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+48}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+75} \lor \neg \left(y \leq 5.8 \cdot 10^{+132}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{-y \cdot t}\\ \end{array} \]

Alternative 7: 73.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-17} \lor \neg \left(y \leq 1.3 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.05e-17) (not (<= y 1.3e+48)))
   (* x (pow z y))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e-17) || !(y <= 1.3e+48)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp((a * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.05d-17)) .or. (.not. (y <= 1.3d+48))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp((a * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e-17) || !(y <= 1.3e+48)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.05e-17) or not (y <= 1.3e+48):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.05e-17) || !(y <= 1.3e+48))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.05e-17) || ~((y <= 1.3e+48)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.05e-17], N[Not[LessEqual[y, 1.3e+48]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.04999999999999996e-17 or 1.29999999999999998e48 < y

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 92.6%

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

   3. Taylor expanded in t around 0 72.9%

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

   if -1.04999999999999996e-17 < y < 1.29999999999999998e48

   1. Initial program 91.7%

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

   2. Taylor expanded in b around inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. *-commutative 79.9%

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

      3. distribute-rgt-neg-in 79.9%

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

   4. Simplified 79.9%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-17} \lor \neg \left(y \leq 1.3 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 8: 60.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-31} \lor \neg \left(y \leq 0.0016\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - b \cdot \left(a - b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.35e-31) (not (<= y 0.0016)))
   (* x (pow z y))
   (* x (- 1.0 (* b (- a (* b (* a (* a 0.5)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.35e-31) || !(y <= 0.0016)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * (1.0 - (b * (a - (b * (a * (a * 0.5))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.35d-31)) .or. (.not. (y <= 0.0016d0))) then
        tmp = x * (z ** y)
    else
        tmp = x * (1.0d0 - (b * (a - (b * (a * (a * 0.5d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.35e-31) || !(y <= 0.0016)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * (1.0 - (b * (a - (b * (a * (a * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.35e-31) or not (y <= 0.0016):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * (1.0 - (b * (a - (b * (a * (a * 0.5))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.35e-31) || !(y <= 0.0016))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * Float64(1.0 - Float64(b * Float64(a - Float64(b * Float64(a * Float64(a * 0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.35e-31) || ~((y <= 0.0016)))
		tmp = x * (z ^ y);
	else
		tmp = x * (1.0 - (b * (a - (b * (a * (a * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.35e-31], N[Not[LessEqual[y, 0.0016]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(b * N[(a - N[(b * N[(a * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.34999999999999993e-31 or 0.00160000000000000008 < y

   1. Initial program 97.8%

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

   2. Taylor expanded in y around inf 89.1%

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

   3. Taylor expanded in t around 0 68.7%

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

   if -2.34999999999999993e-31 < y < 0.00160000000000000008

   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 b around inf 81.5%

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

      1. mul-1-neg 81.5%

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

      2. *-commutative 81.5%

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

      3. distribute-rgt-neg-in 81.5%

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

   4. Simplified 81.5%

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

   5. Taylor expanded in b around 0 53.7%

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

      1. +-commutative 53.7%

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

      2. associate-+r+ 53.7%

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

      3. mul-1-neg 53.7%

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

      4. unsub-neg 53.7%

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

      5. *-commutative 53.7%

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

      6. associate-*r* 53.7%

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

      7. unpow2 53.7%

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

      8. unpow2 53.7%

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

   7. Simplified 53.7%

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

      1. associate-+l- 53.7%

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

      2. *-commutative 53.7%

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

      3. associate-*r* 57.2%

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

      4. distribute-rgt-out-- 57.3%

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

      5. *-commutative 57.3%

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

      6. associate-*l* 57.3%

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

   9. Applied egg-rr 57.3%

      \[\leadsto x \cdot \color{blue}{\left(1 - b \cdot \left(a - \left(a \cdot \left(a \cdot 0.5\right)\right) \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-31} \lor \neg \left(y \leq 0.0016\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - b \cdot \left(a - b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)\\ \end{array} \]

Alternative 9: 42.4% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-160}:\\ \;\;\;\;x - y \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq 11500000:\\ \;\;\;\;x \cdot \left(1 - b \cdot \left(a - b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* 0.5 (* a a)) (* x (* b b)))))
   (if (<= y -6e-41)
     t_1
     (if (<= y -1.1e-160)
       (- x (* y (* x t)))
       (if (<= y 11500000.0)
         (* x (- 1.0 (* b (- a (* b (* a (* a 0.5)))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.5 * (a * a)) * (x * (b * b));
	double tmp;
	if (y <= -6e-41) {
		tmp = t_1;
	} else if (y <= -1.1e-160) {
		tmp = x - (y * (x * t));
	} else if (y <= 11500000.0) {
		tmp = x * (1.0 - (b * (a - (b * (a * (a * 0.5))))));
	} 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 = (0.5d0 * (a * a)) * (x * (b * b))
    if (y <= (-6d-41)) then
        tmp = t_1
    else if (y <= (-1.1d-160)) then
        tmp = x - (y * (x * t))
    else if (y <= 11500000.0d0) then
        tmp = x * (1.0d0 - (b * (a - (b * (a * (a * 0.5d0))))))
    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 = (0.5 * (a * a)) * (x * (b * b));
	double tmp;
	if (y <= -6e-41) {
		tmp = t_1;
	} else if (y <= -1.1e-160) {
		tmp = x - (y * (x * t));
	} else if (y <= 11500000.0) {
		tmp = x * (1.0 - (b * (a - (b * (a * (a * 0.5))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (0.5 * (a * a)) * (x * (b * b))
	tmp = 0
	if y <= -6e-41:
		tmp = t_1
	elif y <= -1.1e-160:
		tmp = x - (y * (x * t))
	elif y <= 11500000.0:
		tmp = x * (1.0 - (b * (a - (b * (a * (a * 0.5))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(0.5 * Float64(a * a)) * Float64(x * Float64(b * b)))
	tmp = 0.0
	if (y <= -6e-41)
		tmp = t_1;
	elseif (y <= -1.1e-160)
		tmp = Float64(x - Float64(y * Float64(x * t)));
	elseif (y <= 11500000.0)
		tmp = Float64(x * Float64(1.0 - Float64(b * Float64(a - Float64(b * Float64(a * Float64(a * 0.5)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (0.5 * (a * a)) * (x * (b * b));
	tmp = 0.0;
	if (y <= -6e-41)
		tmp = t_1;
	elseif (y <= -1.1e-160)
		tmp = x - (y * (x * t));
	elseif (y <= 11500000.0)
		tmp = x * (1.0 - (b * (a - (b * (a * (a * 0.5))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision] * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e-41], t$95$1, If[LessEqual[y, -1.1e-160], N[(x - N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 11500000.0], N[(x * N[(1.0 - N[(b * N[(a - N[(b * N[(a * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999978e-41 or 1.15e7 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in b around inf 40.5%

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

      1. mul-1-neg 40.5%

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

      2. *-commutative 40.5%

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

      3. distribute-rgt-neg-in 40.5%

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

   4. Simplified 40.5%

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

   5. Taylor expanded in b around 0 22.5%

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

      1. +-commutative 22.5%

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

      2. associate-+r+ 22.5%

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

      3. mul-1-neg 22.5%

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

      4. unsub-neg 22.5%

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

      5. *-commutative 22.5%

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

      6. associate-*r* 22.5%

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

      7. unpow2 22.5%

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

      8. unpow2 22.5%

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

   7. Simplified 22.5%

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

   8. Taylor expanded in b around inf 35.0%

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

      1. associate-*r* 35.0%

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

      2. unpow2 35.0%

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

      3. unpow2 35.0%

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

      4. *-commutative 35.0%

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

   10. Simplified 35.0%

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

   if -5.99999999999999978e-41 < y < -1.1e-160

   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 t around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. distribute-rgt-neg-out 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in y around 0 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

   7. Simplified 52.1%

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

   if -1.1e-160 < y < 1.15e7

   1. Initial program 89.2%

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

   2. Taylor expanded in b around inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. *-commutative 79.7%

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

      3. distribute-rgt-neg-in 79.7%

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

   4. Simplified 79.7%

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

   5. Taylor expanded in b around 0 53.4%

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

      1. +-commutative 53.4%

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

      2. associate-+r+ 53.4%

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

      3. mul-1-neg 53.4%

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

      4. unsub-neg 53.4%

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

      5. *-commutative 53.4%

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

      6. associate-*r* 53.4%

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

      7. unpow2 53.4%

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

      8. unpow2 53.4%

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

   7. Simplified 53.4%

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

      1. associate-+l- 53.4%

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

      2. *-commutative 53.4%

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

      3. associate-*r* 57.4%

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

      4. distribute-rgt-out-- 57.5%

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

      5. *-commutative 57.5%

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

      6. associate-*l* 57.5%

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

   9. Applied egg-rr 57.5%

      \[\leadsto x \cdot \color{blue}{\left(1 - b \cdot \left(a - \left(a \cdot \left(a \cdot 0.5\right)\right) \cdot b\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-41}:\\ \;\;\;\;\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-160}:\\ \;\;\;\;x - y \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq 11500000:\\ \;\;\;\;x \cdot \left(1 - b \cdot \left(a - b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \end{array} \]

Alternative 10: 40.4% accurate, 20.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-30} \lor \neg \left(y \leq 11500000\right):\\ \;\;\;\;\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.5e-30) (not (<= y 11500000.0)))
   (* (* 0.5 (* a a)) (* x (* b b)))
   (* x (- 1.0 (* a (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e-30) || !(y <= 11500000.0)) {
		tmp = (0.5 * (a * a)) * (x * (b * b));
	} else {
		tmp = x * (1.0 - (a * (z + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9.5d-30)) .or. (.not. (y <= 11500000.0d0))) then
        tmp = (0.5d0 * (a * a)) * (x * (b * b))
    else
        tmp = x * (1.0d0 - (a * (z + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e-30) || !(y <= 11500000.0)) {
		tmp = (0.5 * (a * a)) * (x * (b * b));
	} else {
		tmp = x * (1.0 - (a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9.5e-30) or not (y <= 11500000.0):
		tmp = (0.5 * (a * a)) * (x * (b * b))
	else:
		tmp = x * (1.0 - (a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9.5e-30) || !(y <= 11500000.0))
		tmp = Float64(Float64(0.5 * Float64(a * a)) * Float64(x * Float64(b * b)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(a * Float64(z + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9.5e-30) || ~((y <= 11500000.0)))
		tmp = (0.5 * (a * a)) * (x * (b * b));
	else
		tmp = x * (1.0 - (a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9.5e-30], N[Not[LessEqual[y, 11500000.0]], $MachinePrecision]], N[(N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision] * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.49999999999999939e-30 or 1.15e7 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in b around inf 39.6%

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

      1. mul-1-neg 39.6%

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

      2. *-commutative 39.6%

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

      3. distribute-rgt-neg-in 39.6%

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

   4. Simplified 39.6%

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

   5. Taylor expanded in b around 0 22.0%

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

      1. +-commutative 22.0%

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

      2. associate-+r+ 22.0%

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

      3. mul-1-neg 22.0%

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

      4. unsub-neg 22.0%

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

      5. *-commutative 22.0%

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

      6. associate-*r* 22.0%

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

      7. unpow2 22.0%

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

      8. unpow2 22.0%

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

   7. Simplified 22.0%

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

   8. Taylor expanded in b around inf 34.8%

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

      1. associate-*r* 34.8%

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

      2. unpow2 34.8%

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

      3. unpow2 34.8%

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

      4. *-commutative 34.8%

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

   10. Simplified 34.8%

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

   if -9.49999999999999939e-30 < y < 1.15e7

   1. Initial program 90.9%

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

   2. Taylor expanded in y around 0 80.7%

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

      1. sub-neg 80.7%

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

      2. neg-mul-1 80.7%

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

      3. log1p-def 89.7%

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

      4. neg-mul-1 89.7%

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

   4. Simplified 89.7%

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

   5. Taylor expanded in z around 0 89.6%

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

      1. associate-*r* 89.6%

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

      2. neg-mul-1 89.6%

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

      3. associate-*r* 89.6%

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

      4. neg-mul-1 89.6%

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

      5. distribute-lft-out 89.6%

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

   7. Simplified 89.6%

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

   8. Taylor expanded in a around 0 48.4%

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

      1. +-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

      4. +-commutative 48.4%

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

   10. Simplified 48.4%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-30} \lor \neg \left(y \leq 11500000\right):\\ \;\;\;\;\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot \left(x \cdot \left(b \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \end{array} \]

Alternative 11: 24.9% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-x\right) \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(-y \cdot t\right)\\ \mathbf{elif}\;a \leq -1.36 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- x) (* a b))))
   (if (<= a -3.4e+171)
     t_1
     (if (<= a -1.4e+42)
       (* x (- (* y t)))
       (if (<= a -1.36e-28) t_1 (if (<= a 6.2e+49) x (* a (* x (- b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -x * (a * b);
	double tmp;
	if (a <= -3.4e+171) {
		tmp = t_1;
	} else if (a <= -1.4e+42) {
		tmp = x * -(y * t);
	} else if (a <= -1.36e-28) {
		tmp = t_1;
	} else if (a <= 6.2e+49) {
		tmp = x;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -x * (a * b)
    if (a <= (-3.4d+171)) then
        tmp = t_1
    else if (a <= (-1.4d+42)) then
        tmp = x * -(y * t)
    else if (a <= (-1.36d-28)) then
        tmp = t_1
    else if (a <= 6.2d+49) then
        tmp = x
    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 t_1 = -x * (a * b);
	double tmp;
	if (a <= -3.4e+171) {
		tmp = t_1;
	} else if (a <= -1.4e+42) {
		tmp = x * -(y * t);
	} else if (a <= -1.36e-28) {
		tmp = t_1;
	} else if (a <= 6.2e+49) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -x * (a * b)
	tmp = 0
	if a <= -3.4e+171:
		tmp = t_1
	elif a <= -1.4e+42:
		tmp = x * -(y * t)
	elif a <= -1.36e-28:
		tmp = t_1
	elif a <= 6.2e+49:
		tmp = x
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-x) * Float64(a * b))
	tmp = 0.0
	if (a <= -3.4e+171)
		tmp = t_1;
	elseif (a <= -1.4e+42)
		tmp = Float64(x * Float64(-Float64(y * t)));
	elseif (a <= -1.36e-28)
		tmp = t_1;
	elseif (a <= 6.2e+49)
		tmp = x;
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -x * (a * b);
	tmp = 0.0;
	if (a <= -3.4e+171)
		tmp = t_1;
	elseif (a <= -1.4e+42)
		tmp = x * -(y * t);
	elseif (a <= -1.36e-28)
		tmp = t_1;
	elseif (a <= 6.2e+49)
		tmp = x;
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-x) * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+171], t$95$1, If[LessEqual[a, -1.4e+42], N[(x * (-N[(y * t), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, -1.36e-28], t$95$1, If[LessEqual[a, 6.2e+49], x, N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.4000000000000001e171 or -1.4e42 < a < -1.35999999999999989e-28

   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 77.2%

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

      1. mul-1-neg 77.2%

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

      2. *-commutative 77.2%

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

      3. distribute-rgt-neg-in 77.2%

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

   4. Simplified 77.2%

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

   5. Taylor expanded in b around 0 35.6%

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

      1. mul-1-neg 35.6%

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

      2. unsub-neg 35.6%

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

      3. *-commutative 35.6%

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

   7. Simplified 35.6%

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

   8. Taylor expanded in b around inf 33.8%

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

      1. mul-1-neg 33.8%

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

      2. associate-*r* 37.8%

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

   10. Simplified 37.8%

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

   if -3.4000000000000001e171 < a < -1.4e42

   1. Initial program 83.7%

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

   2. Taylor expanded in t around inf 39.2%

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

      1. mul-1-neg 39.2%

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

      2. distribute-rgt-neg-out 39.2%

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

   4. Simplified 39.2%

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

   5. Taylor expanded in y around 0 11.4%

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

      1. +-commutative 11.4%

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

      2. mul-1-neg 11.4%

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

      3. unsub-neg 11.4%

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

   7. Simplified 11.4%

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

   8. Taylor expanded in y around inf 23.2%

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

      1. mul-1-neg 23.2%

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

      2. associate-*r* 27.4%

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

      3. distribute-rgt-neg-in 27.4%

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

   10. Simplified 27.4%

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

   if -1.35999999999999989e-28 < a < 6.19999999999999985e49

   1. Initial program 99.5%

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

   2. Taylor expanded in b around inf 49.2%

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

      1. mul-1-neg 49.2%

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

      2. *-commutative 49.2%

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

      3. distribute-rgt-neg-in 49.2%

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

   4. Simplified 49.2%

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

   5. Taylor expanded in b around 0 31.3%

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

   if 6.19999999999999985e49 < a

   1. Initial program 89.2%

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

   2. Taylor expanded in b around inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. *-commutative 64.7%

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

      3. distribute-rgt-neg-in 64.7%

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

   4. Simplified 64.7%

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

   5. Taylor expanded in b around 0 32.3%

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

      1. mul-1-neg 32.3%

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

      2. unsub-neg 32.3%

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

      3. *-commutative 32.3%

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

   7. Simplified 32.3%

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

   8. Taylor expanded in b around inf 32.1%

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

      1. mul-1-neg 32.1%

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

      2. distribute-rgt-neg-in 32.1%

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

   10. Simplified 32.1%

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

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+171}:\\ \;\;\;\;\left(-x\right) \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(-y \cdot t\right)\\ \mathbf{elif}\;a \leq -1.36 \cdot 10^{-28}:\\ \;\;\;\;\left(-x\right) \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 12: 33.3% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(-y \cdot t\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.5e+56)
   (* x (- (* y t)))
   (if (<= y 1.85e-6) (* x (- 1.0 (* a (+ z b)))) (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.5e+56) {
		tmp = x * -(y * t);
	} else if (y <= 1.85e-6) {
		tmp = x * (1.0 - (a * (z + b)));
	} 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 (y <= (-6.5d+56)) then
        tmp = x * -(y * t)
    else if (y <= 1.85d-6) then
        tmp = x * (1.0d0 - (a * (z + b)))
    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 (y <= -6.5e+56) {
		tmp = x * -(y * t);
	} else if (y <= 1.85e-6) {
		tmp = x * (1.0 - (a * (z + b)));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.5e+56:
		tmp = x * -(y * t)
	elif y <= 1.85e-6:
		tmp = x * (1.0 - (a * (z + b)))
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.5e+56)
		tmp = Float64(x * Float64(-Float64(y * t)));
	elseif (y <= 1.85e-6)
		tmp = Float64(x * Float64(1.0 - Float64(a * Float64(z + b))));
	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 (y <= -6.5e+56)
		tmp = x * -(y * t);
	elseif (y <= 1.85e-6)
		tmp = x * (1.0 - (a * (z + b)));
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.5e+56], N[(x * (-N[(y * t), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 1.85e-6], N[(x * N[(1.0 - N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5000000000000001e56

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. distribute-rgt-neg-out 62.5%

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

   4. Simplified 62.5%

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

   5. Taylor expanded in y around 0 18.9%

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

      1. +-commutative 18.9%

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

      2. mul-1-neg 18.9%

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

      3. unsub-neg 18.9%

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

   7. Simplified 18.9%

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

   8. Taylor expanded in y around inf 18.2%

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

      1. mul-1-neg 18.2%

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

      2. associate-*r* 22.0%

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

      3. distribute-rgt-neg-in 22.0%

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

   10. Simplified 22.0%

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

   if -6.5000000000000001e56 < y < 1.8500000000000001e-6

   1. Initial program 91.9%

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

   2. Taylor expanded in y around 0 78.1%

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

      1. sub-neg 78.1%

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

      2. neg-mul-1 78.1%

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

      3. log1p-def 86.0%

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

      4. neg-mul-1 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in z around 0 85.8%

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

      1. associate-*r* 85.8%

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

      2. neg-mul-1 85.8%

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

      3. associate-*r* 85.8%

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

      4. neg-mul-1 85.8%

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

      5. distribute-lft-out 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in a around 0 45.3%

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

      1. +-commutative 45.3%

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

      2. mul-1-neg 45.3%

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

      3. unsub-neg 45.3%

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

      4. +-commutative 45.3%

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

   10. Simplified 45.3%

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

   if 1.8500000000000001e-6 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in b around inf 39.8%

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

      1. mul-1-neg 39.8%

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

      2. *-commutative 39.8%

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

      3. distribute-rgt-neg-in 39.8%

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

   4. Simplified 39.8%

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

   5. Taylor expanded in b around 0 14.9%

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

      1. mul-1-neg 14.9%

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

      2. unsub-neg 14.9%

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

      3. *-commutative 14.9%

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

   7. Simplified 14.9%

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

   8. Taylor expanded in b around inf 26.4%

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

      1. mul-1-neg 26.4%

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

      2. distribute-rgt-neg-in 26.4%

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

   10. Simplified 26.4%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(-y \cdot t\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 13: 33.0% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(-y \cdot t\right)\\ \mathbf{elif}\;y \leq 0.0017:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.8e+56)
   (* x (- (* y t)))
   (if (<= y 0.0017) (* x (- 1.0 (* a b))) (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.8e+56) {
		tmp = x * -(y * t);
	} else if (y <= 0.0017) {
		tmp = x * (1.0 - (a * b));
	} 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 (y <= (-6.8d+56)) then
        tmp = x * -(y * t)
    else if (y <= 0.0017d0) then
        tmp = x * (1.0d0 - (a * b))
    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 (y <= -6.8e+56) {
		tmp = x * -(y * t);
	} else if (y <= 0.0017) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.8e+56:
		tmp = x * -(y * t)
	elif y <= 0.0017:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.8e+56)
		tmp = Float64(x * Float64(-Float64(y * t)));
	elseif (y <= 0.0017)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	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 (y <= -6.8e+56)
		tmp = x * -(y * t);
	elseif (y <= 0.0017)
		tmp = x * (1.0 - (a * b));
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.8e+56], N[(x * (-N[(y * t), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 0.0017], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.80000000000000002e56

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. distribute-rgt-neg-out 62.5%

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

   4. Simplified 62.5%

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

   5. Taylor expanded in y around 0 18.9%

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

      1. +-commutative 18.9%

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

      2. mul-1-neg 18.9%

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

      3. unsub-neg 18.9%

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

   7. Simplified 18.9%

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

   8. Taylor expanded in y around inf 18.2%

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

      1. mul-1-neg 18.2%

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

      2. associate-*r* 22.0%

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

      3. distribute-rgt-neg-in 22.0%

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

   10. Simplified 22.0%

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

   if -6.80000000000000002e56 < y < 0.00169999999999999991

   1. Initial program 92.0%

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

   2. Taylor expanded in b around inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. *-commutative 76.7%

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

      3. distribute-rgt-neg-in 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in b around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. unsub-neg 44.4%

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

      3. *-commutative 44.4%

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

   7. Simplified 44.4%

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

   if 0.00169999999999999991 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in b around inf 40.4%

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

      1. mul-1-neg 40.4%

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

      2. *-commutative 40.4%

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

      3. distribute-rgt-neg-in 40.4%

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

   4. Simplified 40.4%

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

   5. Taylor expanded in b around 0 15.1%

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

      1. mul-1-neg 15.1%

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

      2. unsub-neg 15.1%

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

      3. *-commutative 15.1%

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

   7. Simplified 15.1%

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

   8. Taylor expanded in b around inf 26.8%

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

      1. mul-1-neg 26.8%

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

      2. distribute-rgt-neg-in 26.8%

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

   10. Simplified 26.8%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(-y \cdot t\right)\\ \mathbf{elif}\;y \leq 0.0017:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 14: 23.7% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+181} \lor \neg \left(a \leq 1.05 \cdot 10^{+16}\right):\\ \;\;\;\;-b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.2e+181) (not (<= a 1.05e+16))) (- (* b (* x a))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.2e+181) || !(a <= 1.05e+16)) {
		tmp = -(b * (x * a));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-3.2d+181)) .or. (.not. (a <= 1.05d+16))) then
        tmp = -(b * (x * a))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.2e+181) || !(a <= 1.05e+16)) {
		tmp = -(b * (x * a));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.2e+181) or not (a <= 1.05e+16):
		tmp = -(b * (x * a))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.2e+181) || !(a <= 1.05e+16))
		tmp = Float64(-Float64(b * Float64(x * a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3.2e+181) || ~((a <= 1.05e+16)))
		tmp = -(b * (x * a));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.2e+181], N[Not[LessEqual[a, 1.05e+16]], $MachinePrecision]], (-N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), x]

Derivation

1. Split input into 2 regimes

2. if a < -3.2e181 or 1.05e16 < a

   1. Initial program 91.8%

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

   2. Taylor expanded in b around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. *-commutative 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

   4. Simplified 72.0%

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

   5. Taylor expanded in b around 0 34.6%

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

      1. mul-1-neg 34.6%

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

      2. unsub-neg 34.6%

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

      3. *-commutative 34.6%

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

   7. Simplified 34.6%

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

   8. Taylor expanded in b around inf 33.6%

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

      1. mul-1-neg 33.6%

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

      2. associate-*r* 33.6%

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

   10. Simplified 33.6%

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

   11. Taylor expanded in a around 0 33.6%

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

       1. associate-*r* 33.6%

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

       2. *-commutative 33.6%

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

       3. associate-*l* 30.2%

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

   13. Simplified 30.2%

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

   if -3.2e181 < a < 1.05e16

   1. Initial program 96.9%

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

   2. Taylor expanded in b around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. *-commutative 50.6%

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

      3. distribute-rgt-neg-in 50.6%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in b around 0 26.2%

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

4. Final simplification 27.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+181} \lor \neg \left(a \leq 1.05 \cdot 10^{+16}\right):\\ \;\;\;\;-b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 24.8% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-25} \lor \neg \left(a \leq 9.5 \cdot 10^{+84}\right):\\ \;\;\;\;\left(-x\right) \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -8.6e-25) (not (<= a 9.5e+84))) (* (- x) (* a b)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8.6e-25) || !(a <= 9.5e+84)) {
		tmp = -x * (a * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-8.6d-25)) .or. (.not. (a <= 9.5d+84))) then
        tmp = -x * (a * b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8.6e-25) || !(a <= 9.5e+84)) {
		tmp = -x * (a * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -8.6e-25) or not (a <= 9.5e+84):
		tmp = -x * (a * b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -8.6e-25) || !(a <= 9.5e+84))
		tmp = Float64(Float64(-x) * Float64(a * b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -8.6e-25) || ~((a <= 9.5e+84)))
		tmp = -x * (a * b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -8.6e-25], N[Not[LessEqual[a, 9.5e+84]], $MachinePrecision]], N[((-x) * N[(a * b), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -8.59999999999999953e-25 or 9.49999999999999979e84 < a

   1. Initial program 90.5%

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

   2. Taylor expanded in b around inf 68.8%

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

      1. mul-1-neg 68.8%

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

      2. *-commutative 68.8%

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

      3. distribute-rgt-neg-in 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in b around 0 27.8%

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

      1. mul-1-neg 27.8%

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

      2. unsub-neg 27.8%

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

      3. *-commutative 27.8%

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

   7. Simplified 27.8%

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

   8. Taylor expanded in b around inf 28.5%

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

      1. mul-1-neg 28.5%

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

      2. associate-*r* 29.2%

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

   10. Simplified 29.2%

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

   if -8.59999999999999953e-25 < a < 9.49999999999999979e84

   1. Initial program 98.8%

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

   2. Taylor expanded in b around inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. *-commutative 50.8%

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

      3. distribute-rgt-neg-in 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in b around 0 30.7%

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

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-25} \lor \neg \left(a \leq 9.5 \cdot 10^{+84}\right):\\ \;\;\;\;\left(-x\right) \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 25.1% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{-27}:\\ \;\;\;\;\left(-x\right) \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.22e-27)
   (* (- x) (* a b))
   (if (<= a 9.5e+49) x (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.22e-27) {
		tmp = -x * (a * b);
	} else if (a <= 9.5e+49) {
		tmp = x;
	} 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 <= (-1.22d-27)) then
        tmp = -x * (a * b)
    else if (a <= 9.5d+49) then
        tmp = x
    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 <= -1.22e-27) {
		tmp = -x * (a * b);
	} else if (a <= 9.5e+49) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.22e-27:
		tmp = -x * (a * b)
	elif a <= 9.5e+49:
		tmp = x
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.22e-27)
		tmp = Float64(Float64(-x) * Float64(a * b));
	elseif (a <= 9.5e+49)
		tmp = x;
	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 <= -1.22e-27)
		tmp = -x * (a * b);
	elseif (a <= 9.5e+49)
		tmp = x;
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.22e-27], N[((-x) * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+49], x, N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.22e-27

   1. Initial program 91.7%

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

   2. Taylor expanded in b around inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. *-commutative 72.7%

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

      3. distribute-rgt-neg-in 72.7%

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

   4. Simplified 72.7%

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

   5. Taylor expanded in b around 0 26.0%

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

      1. mul-1-neg 26.0%

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

      2. unsub-neg 26.0%

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

      3. *-commutative 26.0%

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

   7. Simplified 26.0%

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

   8. Taylor expanded in b around inf 25.9%

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

      1. mul-1-neg 25.9%

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

      2. associate-*r* 27.2%

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

   10. Simplified 27.2%

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

   if -1.22e-27 < a < 9.49999999999999969e49

   1. Initial program 99.5%

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

   2. Taylor expanded in b around inf 49.2%

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

      1. mul-1-neg 49.2%

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

      2. *-commutative 49.2%

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

      3. distribute-rgt-neg-in 49.2%

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

   4. Simplified 49.2%

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

   5. Taylor expanded in b around 0 31.3%

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

   if 9.49999999999999969e49 < a

   1. Initial program 89.2%

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

   2. Taylor expanded in b around inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. *-commutative 64.7%

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

      3. distribute-rgt-neg-in 64.7%

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

   4. Simplified 64.7%

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

   5. Taylor expanded in b around 0 32.3%

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

      1. mul-1-neg 32.3%

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

      2. unsub-neg 32.3%

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

      3. *-commutative 32.3%

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

   7. Simplified 32.3%

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

   8. Taylor expanded in b around inf 32.1%

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

      1. mul-1-neg 32.1%

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

      2. distribute-rgt-neg-in 32.1%

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

   10. Simplified 32.1%

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

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{-27}:\\ \;\;\;\;\left(-x\right) \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 17: 19.2% 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 94.8%

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

2. Taylor expanded in b around inf 59.5%

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

   1. mul-1-neg 59.5%

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

   2. *-commutative 59.5%

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

   3. distribute-rgt-neg-in 59.5%

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

4. Simplified 59.5%

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

5. Taylor expanded in b around 0 18.1%

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

6. Final simplification 18.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023181 
(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))))))