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

Percentage Accurate: 96.6% → 99.6%

Time: 14.5s

Alternatives: 15

Speedup: 1.0×

• 41.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.8%

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

   1. fma-define 96.2%

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

   2. sub-neg 96.2%

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

   3. log1p-define 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.8%

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

Alternative 3: 82.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00026 \lor \neg \left(a \leq 13\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -0.00026) (not (<= a 13.0)))
   (* x (exp (* a (- (log1p (- z)) b))))
   (* x (exp (* y (- (log z) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -0.00026) || !(a <= 13.0)) {
		tmp = x * exp((a * (log1p(-z) - b)));
	} else {
		tmp = x * exp((y * (log(z) - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -0.00026) || !(a <= 13.0)) {
		tmp = x * Math.exp((a * (Math.log1p(-z) - b)));
	} else {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -0.00026) or not (a <= 13.0):
		tmp = x * math.exp((a * (math.log1p(-z) - b)))
	else:
		tmp = x * math.exp((y * (math.log(z) - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -0.00026) || !(a <= 13.0))
		tmp = Float64(x * exp(Float64(a * Float64(log1p(Float64(-z)) - b))));
	else
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -0.00026], N[Not[LessEqual[a, 13.0]], $MachinePrecision]], N[(x * N[Exp[N[(a * N[(N[Log[1 + (-z)], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.59999999999999977e-4 or 13 < a

   1. Initial program 91.3%

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

   3. Taylor expanded in y around 0 78.9%

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

      1. sub-neg 78.9%

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

      2. mul-1-neg 78.9%

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

      3. log1p-define 86.8%

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

      4. mul-1-neg 86.8%

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

   5. Simplified 86.8%

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

   if -2.59999999999999977e-4 < a < 13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 91.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00026 \lor \neg \left(a \leq 13\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-5} \lor \neg \left(a \leq 13\right):\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.15e-5) (not (<= a 13.0)))
   (/ x (exp (* a b)))
   (* x (exp (* y (- (log z) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.15e-5) || !(a <= 13.0)) {
		tmp = x / exp((a * b));
	} else {
		tmp = x * exp((y * (log(z) - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.15d-5)) .or. (.not. (a <= 13.0d0))) then
        tmp = x / exp((a * b))
    else
        tmp = x * exp((y * (log(z) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.15e-5) || !(a <= 13.0)) {
		tmp = x / Math.exp((a * b));
	} else {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.15e-5) or not (a <= 13.0):
		tmp = x / math.exp((a * b))
	else:
		tmp = x * math.exp((y * (math.log(z) - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.15e-5) || !(a <= 13.0))
		tmp = Float64(x / exp(Float64(a * b)));
	else
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.15e-5) || ~((a <= 13.0)))
		tmp = x / exp((a * b));
	else
		tmp = x * exp((y * (log(z) - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.15e-5], N[Not[LessEqual[a, 13.0]], $MachinePrecision]], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.15e-5 or 13 < a

   1. Initial program 91.3%

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

   3. Taylor expanded in b around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. distribute-rgt-neg-out 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in a around inf 78.9%

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

      1. neg-mul-1 78.9%

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

      2. distribute-rgt-neg-in 78.9%

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

      3. exp-prod 77.1%

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

   8. Simplified 77.1%

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

      1. pow-neg 77.1%

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

      2. un-div-inv 77.1%

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

   10. Applied egg-rr 77.1%

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

   11. Taylor expanded in a around inf 78.9%

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

   if -1.15e-5 < a < 13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 91.6%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-5} \lor \neg \left(a \leq 13\right):\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.47:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+83} \lor \neg \left(y \leq 5 \cdot 10^{+114}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -4.5e-14)
     t_1
     (if (<= y 0.47)
       (/ x (+ 1.0 (* a b)))
       (if (or (<= y 4e+83) (not (<= y 5e+114))) t_1 (* x (- 1.0 (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -4.5e-14) {
		tmp = t_1;
	} else if (y <= 0.47) {
		tmp = x / (1.0 + (a * b));
	} else if ((y <= 4e+83) || !(y <= 5e+114)) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-4.5d-14)) then
        tmp = t_1
    else if (y <= 0.47d0) then
        tmp = x / (1.0d0 + (a * b))
    else if ((y <= 4d+83) .or. (.not. (y <= 5d+114))) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -4.5e-14) {
		tmp = t_1;
	} else if (y <= 0.47) {
		tmp = x / (1.0 + (a * b));
	} else if ((y <= 4e+83) || !(y <= 5e+114)) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -4.5e-14:
		tmp = t_1
	elif y <= 0.47:
		tmp = x / (1.0 + (a * b))
	elif (y <= 4e+83) or not (y <= 5e+114):
		tmp = t_1
	else:
		tmp = x * (1.0 - (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -4.5e-14)
		tmp = t_1;
	elseif (y <= 0.47)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	elseif ((y <= 4e+83) || !(y <= 5e+114))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -4.5e-14)
		tmp = t_1;
	elseif (y <= 0.47)
		tmp = x / (1.0 + (a * b));
	elseif ((y <= 4e+83) || ~((y <= 5e+114)))
		tmp = t_1;
	else
		tmp = x * (1.0 - (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e-14], t$95$1, If[LessEqual[y, 0.47], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 4e+83], N[Not[LessEqual[y, 5e+114]], $MachinePrecision]], t$95$1, N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4999999999999998e-14 or 0.46999999999999997 < y < 4.00000000000000012e83 or 5.0000000000000001e114 < y

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 90.3%

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

   4. Taylor expanded in t around 0 69.3%

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

   if -4.4999999999999998e-14 < y < 0.46999999999999997

   1. Initial program 92.2%

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

   3. Taylor expanded in b around inf 78.2%

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

      1. mul-1-neg 78.2%

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

      2. distribute-rgt-neg-out 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in a around inf 78.2%

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

      1. neg-mul-1 78.2%

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

      2. distribute-rgt-neg-in 78.2%

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

      3. exp-prod 65.6%

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

   8. Simplified 65.6%

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

      1. pow-neg 65.6%

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

      2. un-div-inv 65.6%

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

   10. Applied egg-rr 65.6%

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

   11. Taylor expanded in a around 0 52.1%

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

   if 4.00000000000000012e83 < y < 5.0000000000000001e114

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 87.8%

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

      1. mul-1-neg 87.8%

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

      2. distribute-rgt-neg-out 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in a around 0 52.0%

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

      1. neg-mul-1 52.0%

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

      2. unsub-neg 52.0%

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

   8. Simplified 52.0%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 0.47:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+83} \lor \neg \left(y \leq 5 \cdot 10^{+114}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{-89} \lor \neg \left(a \leq 0.000114\right):\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -9.8e-89) (not (<= a 0.000114)))
   (/ x (exp (* a b)))
   (* x (exp (* t (- y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -9.8e-89) || !(a <= 0.000114)) {
		tmp = x / exp((a * b));
	} else {
		tmp = x * exp((t * -y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-9.8d-89)) .or. (.not. (a <= 0.000114d0))) then
        tmp = x / exp((a * b))
    else
        tmp = x * exp((t * -y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -9.8e-89) || !(a <= 0.000114)) {
		tmp = x / Math.exp((a * b));
	} else {
		tmp = x * Math.exp((t * -y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -9.8e-89) or not (a <= 0.000114):
		tmp = x / math.exp((a * b))
	else:
		tmp = x * math.exp((t * -y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -9.8e-89) || !(a <= 0.000114))
		tmp = Float64(x / exp(Float64(a * b)));
	else
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -9.8e-89) || ~((a <= 0.000114)))
		tmp = x / exp((a * b));
	else
		tmp = x * exp((t * -y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -9.8e-89], N[Not[LessEqual[a, 0.000114]], $MachinePrecision]], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.8e-89 or 1.1400000000000001e-4 < a

   1. Initial program 92.2%

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

   3. Taylor expanded in b around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-rgt-neg-out 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in a around inf 76.3%

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

      1. neg-mul-1 76.3%

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

      2. distribute-rgt-neg-in 76.3%

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

      3. exp-prod 72.0%

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

   8. Simplified 72.0%

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

      1. pow-neg 72.0%

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

      2. un-div-inv 72.0%

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

   10. Applied egg-rr 72.0%

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

   11. Taylor expanded in a around inf 76.3%

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

   if -9.8e-89 < a < 1.1400000000000001e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 78.0%

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

      1. mul-1-neg 78.0%

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

      2. distribute-lft-neg-out 78.0%

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

      3. *-commutative 78.0%

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

   5. Simplified 78.0%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{-89} \lor \neg \left(a \leq 0.000114\right):\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.016 \lor \neg \left(y \leq 4.5 \cdot 10^{+123}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.016) (not (<= y 4.5e+123)))
   (* 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 <= -0.016) || !(y <= 4.5e+123)) {
		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 <= (-0.016d0)) .or. (.not. (y <= 4.5d+123))) 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 <= -0.016) || !(y <= 4.5e+123)) {
		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 <= -0.016) or not (y <= 4.5e+123):
		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 <= -0.016) || !(y <= 4.5e+123))
		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 <= -0.016) || ~((y <= 4.5e+123)))
		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, -0.016], N[Not[LessEqual[y, 4.5e+123]], $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 < -0.016 or 4.49999999999999983e123 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 93.2%

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

   4. Taylor expanded in t around 0 73.7%

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

   if -0.016 < y < 4.49999999999999983e123

   1. Initial program 93.7%

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

   3. Taylor expanded in b around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. distribute-rgt-neg-out 74.0%

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

   5. Simplified 74.0%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.016 \lor \neg \left(y \leq 4.5 \cdot 10^{+123}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0135 \lor \neg \left(y \leq 3.2 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.0135) (not (<= y 3.2e+125)))
   (* 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 <= -0.0135) || !(y <= 3.2e+125)) {
		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 <= (-0.0135d0)) .or. (.not. (y <= 3.2d+125))) 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 <= -0.0135) || !(y <= 3.2e+125)) {
		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 <= -0.0135) or not (y <= 3.2e+125):
		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 <= -0.0135) || !(y <= 3.2e+125))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x / exp(Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -0.0135) || ~((y <= 3.2e+125)))
		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, -0.0135], N[Not[LessEqual[y, 3.2e+125]], $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 < -0.0134999999999999998 or 3.19999999999999983e125 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 93.2%

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

   4. Taylor expanded in t around 0 73.7%

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

   if -0.0134999999999999998 < y < 3.19999999999999983e125

   1. Initial program 93.7%

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

   3. Taylor expanded in b around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. distribute-rgt-neg-out 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in a around inf 74.0%

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

      1. neg-mul-1 74.0%

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

      2. distribute-rgt-neg-in 74.0%

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

      3. exp-prod 62.6%

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

   8. Simplified 62.6%

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

      1. pow-neg 62.6%

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

      2. un-div-inv 62.6%

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

   10. Applied egg-rr 62.6%

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

   11. Taylor expanded in a around inf 74.0%

       \[\leadsto \frac{x}{\color{blue}{e^{a \cdot b}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0135 \lor \neg \left(y \leq 3.2 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.6% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.8e-43)
   (* x (- 1.0 (* a b)))
   (if (<= b 6e+16) (* x (- 1.0 (* y t))) (* t (* x (- y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.8e-43) {
		tmp = x * (1.0 - (a * b));
	} else if (b <= 6e+16) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = t * (x * -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.8d-43)) then
        tmp = x * (1.0d0 - (a * b))
    else if (b <= 6d+16) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = t * (x * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.8e-43) {
		tmp = x * (1.0 - (a * b));
	} else if (b <= 6e+16) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = t * (x * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.8e-43:
		tmp = x * (1.0 - (a * b))
	elif b <= 6e+16:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = t * (x * -y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.8e-43)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (b <= 6e+16)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(t * Float64(x * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.8e-43)
		tmp = x * (1.0 - (a * b));
	elseif (b <= 6e+16)
		tmp = x * (1.0 - (y * t));
	else
		tmp = t * (x * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.8e-43], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e+16], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.80000000000000001e-43

   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. Add Preprocessing

   3. Taylor expanded in b around inf 67.1%

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

      1. mul-1-neg 67.1%

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

      2. distribute-rgt-neg-out 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in a around 0 24.9%

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

      1. neg-mul-1 24.9%

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

      2. unsub-neg 24.9%

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

   8. Simplified 24.9%

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

   if -7.80000000000000001e-43 < b < 6e16

   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. Add Preprocessing

   3. Taylor expanded in t around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. distribute-lft-neg-out 74.7%

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

      3. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in y around 0 40.6%

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

      1. associate-*r* 40.6%

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

      2. mul-1-neg 40.6%

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

      3. cancel-sign-sub-inv 40.6%

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

   8. Simplified 40.6%

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

   if 6e16 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 46.8%

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

      1. mul-1-neg 46.8%

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

      2. distribute-lft-neg-out 46.8%

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

      3. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in y around 0 17.8%

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

      1. associate-*r* 17.8%

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

      2. mul-1-neg 17.8%

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

      3. cancel-sign-sub-inv 17.8%

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

   8. Simplified 17.8%

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

   9. Taylor expanded in t around inf 33.3%

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

       1. mul-1-neg 33.3%

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

       2. distribute-rgt-neg-in 33.3%

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

       3. distribute-rgt-neg-in 33.3%

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

   11. Simplified 33.3%

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

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 21.2% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.4e+45) (* t (* x y)) (if (<= b 2.6e-45) x (* x (* t (- y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.4e+45) {
		tmp = t * (x * y);
	} else if (b <= 2.6e-45) {
		tmp = x;
	} else {
		tmp = x * (t * -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.4d+45)) then
        tmp = t * (x * y)
    else if (b <= 2.6d-45) then
        tmp = x
    else
        tmp = x * (t * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.4e+45) {
		tmp = t * (x * y);
	} else if (b <= 2.6e-45) {
		tmp = x;
	} else {
		tmp = x * (t * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.4e+45:
		tmp = t * (x * y)
	elif b <= 2.6e-45:
		tmp = x
	else:
		tmp = x * (t * -y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.4e+45)
		tmp = Float64(t * Float64(x * y));
	elseif (b <= 2.6e-45)
		tmp = x;
	else
		tmp = Float64(x * Float64(t * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.4e+45)
		tmp = t * (x * y);
	elseif (b <= 2.6e-45)
		tmp = x;
	else
		tmp = x * (t * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.4e+45], N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e-45], x, N[(x * N[(t * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.39999999999999968e45

   1. Initial program 97.9%

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

   3. Taylor expanded in t around inf 38.2%

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

      1. mul-1-neg 38.2%

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

      2. distribute-lft-neg-out 38.2%

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

      3. *-commutative 38.2%

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

   5. Simplified 38.2%

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

   6. Taylor expanded in y around 0 5.8%

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

      1. associate-*r* 5.8%

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

      2. mul-1-neg 5.8%

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

      3. cancel-sign-sub-inv 5.8%

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

   8. Simplified 5.8%

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

   9. Taylor expanded in t around inf 12.5%

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

       1. mul-1-neg 12.5%

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

       2. distribute-rgt-neg-in 12.5%

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

       3. distribute-rgt-neg-in 12.5%

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

   11. Simplified 12.5%

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

       1. pow1 12.5%

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

       2. add-sqr-sqrt 5.4%

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

       3. sqrt-unprod 16.4%

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

       4. sqr-neg 16.4%

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

       5. sqrt-unprod 7.3%

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

       6. add-sqr-sqrt 14.4%

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

   13. Applied egg-rr 14.4%

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

       1. unpow1 14.4%

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

   15. Simplified 14.4%

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

   if -5.39999999999999968e45 < b < 2.59999999999999987e-45

   1. Initial program 92.8%

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

   3. Taylor expanded in t around inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. distribute-lft-neg-out 71.8%

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

      3. *-commutative 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in y around 0 32.4%

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

   if 2.59999999999999987e-45 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. distribute-lft-neg-out 53.6%

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

      3. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in y around 0 21.0%

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

      1. associate-*r* 21.0%

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

      2. mul-1-neg 21.0%

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

      3. cancel-sign-sub-inv 21.0%

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

   8. Simplified 21.0%

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

   9. Taylor expanded in t around inf 31.5%

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

       1. mul-1-neg 31.5%

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

       2. associate-*r* 29.9%

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

       3. distribute-rgt-neg-in 29.9%

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

       4. *-commutative 29.9%

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

       5. associate-*r* 32.5%

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

   11. Simplified 32.5%

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

Alternative 11: 21.2% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.5e+45) (* t (* x y)) (if (<= b 2.1e-7) x (* t (* x (- y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.5e+45) {
		tmp = t * (x * y);
	} else if (b <= 2.1e-7) {
		tmp = x;
	} else {
		tmp = t * (x * -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.5d+45)) then
        tmp = t * (x * y)
    else if (b <= 2.1d-7) then
        tmp = x
    else
        tmp = t * (x * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.5e+45) {
		tmp = t * (x * y);
	} else if (b <= 2.1e-7) {
		tmp = x;
	} else {
		tmp = t * (x * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.5e+45:
		tmp = t * (x * y)
	elif b <= 2.1e-7:
		tmp = x
	else:
		tmp = t * (x * -y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.5e+45)
		tmp = Float64(t * Float64(x * y));
	elseif (b <= 2.1e-7)
		tmp = x;
	else
		tmp = Float64(t * Float64(x * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.5e+45)
		tmp = t * (x * y);
	elseif (b <= 2.1e-7)
		tmp = x;
	else
		tmp = t * (x * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.5e+45], N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-7], x, N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.5000000000000001e45

   1. Initial program 97.9%

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

   3. Taylor expanded in t around inf 38.2%

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

      1. mul-1-neg 38.2%

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

      2. distribute-lft-neg-out 38.2%

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

      3. *-commutative 38.2%

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

   5. Simplified 38.2%

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

   6. Taylor expanded in y around 0 5.8%

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

      1. associate-*r* 5.8%

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

      2. mul-1-neg 5.8%

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

      3. cancel-sign-sub-inv 5.8%

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

   8. Simplified 5.8%

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

   9. Taylor expanded in t around inf 12.5%

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

       1. mul-1-neg 12.5%

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

       2. distribute-rgt-neg-in 12.5%

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

       3. distribute-rgt-neg-in 12.5%

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

   11. Simplified 12.5%

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

       1. pow1 12.5%

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

       2. add-sqr-sqrt 5.4%

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

       3. sqrt-unprod 16.4%

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

       4. sqr-neg 16.4%

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

       5. sqrt-unprod 7.3%

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

       6. add-sqr-sqrt 14.4%

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

   13. Applied egg-rr 14.4%

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

       1. unpow1 14.4%

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

   15. Simplified 14.4%

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

   if -5.5000000000000001e45 < b < 2.1e-7

   1. Initial program 93.2%

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

   3. Taylor expanded in t around inf 72.5%

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

      1. mul-1-neg 72.5%

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

      2. distribute-lft-neg-out 72.5%

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

      3. *-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in y around 0 31.7%

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

   if 2.1e-7 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. distribute-lft-neg-out 50.1%

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

      3. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in y around 0 18.5%

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

      1. associate-*r* 18.5%

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

      2. mul-1-neg 18.5%

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

      3. cancel-sign-sub-inv 18.5%

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

   8. Simplified 18.5%

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

   9. Taylor expanded in t around inf 33.1%

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

       1. mul-1-neg 33.1%

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

       2. distribute-rgt-neg-in 33.1%

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

       3. distribute-rgt-neg-in 33.1%

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

   11. Simplified 33.1%

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

Alternative 12: 19.7% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+45} \lor \neg \left(b \leq 3.6 \cdot 10^{+20}\right):\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.5e+45) (not (<= b 3.6e+20))) (* t (* x y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.5e+45) || !(b <= 3.6e+20)) {
		tmp = t * (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5.5d+45)) .or. (.not. (b <= 3.6d+20))) then
        tmp = t * (x * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.5e+45) || !(b <= 3.6e+20)) {
		tmp = t * (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.5e+45) or not (b <= 3.6e+20):
		tmp = t * (x * y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.5e+45) || !(b <= 3.6e+20))
		tmp = Float64(t * Float64(x * y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.5e+45) || ~((b <= 3.6e+20)))
		tmp = t * (x * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.5e+45], N[Not[LessEqual[b, 3.6e+20]], $MachinePrecision]], N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -5.5000000000000001e45 or 3.6e20 < b

   1. Initial program 99.1%

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

   3. Taylor expanded in t around inf 42.9%

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

      1. mul-1-neg 42.9%

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

      2. distribute-lft-neg-out 42.9%

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

      3. *-commutative 42.9%

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

   5. Simplified 42.9%

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

   6. Taylor expanded in y around 0 12.5%

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

      1. associate-*r* 12.5%

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

      2. mul-1-neg 12.5%

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

      3. cancel-sign-sub-inv 12.5%

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

   8. Simplified 12.5%

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

   9. Taylor expanded in t around inf 24.1%

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

       1. mul-1-neg 24.1%

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

       2. distribute-rgt-neg-in 24.1%

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

       3. distribute-rgt-neg-in 24.1%

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

   11. Simplified 24.1%

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

       1. pow1 24.1%

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

       2. add-sqr-sqrt 13.0%

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

       3. sqrt-unprod 28.2%

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

       4. sqr-neg 28.2%

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

       5. sqrt-unprod 9.2%

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

       6. add-sqr-sqrt 20.9%

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

   13. Applied egg-rr 20.9%

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

       1. unpow1 20.9%

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

   15. Simplified 20.9%

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

   if -5.5000000000000001e45 < b < 3.6e20

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf 73.2%

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

      1. mul-1-neg 73.2%

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

      2. distribute-lft-neg-out 73.2%

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

      3. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in y around 0 31.0%

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

4. Final simplification 26.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+45} \lor \neg \left(b \leq 3.6 \cdot 10^{+20}\right):\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.5% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.4 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 4.4e-60) (/ x (+ 1.0 (* a b))) (- x (* t (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.4e-60) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = x - (t * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 4.4d-60) then
        tmp = x / (1.0d0 + (a * b))
    else
        tmp = x - (t * (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.4e-60) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = x - (t * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 4.4e-60:
		tmp = x / (1.0 + (a * b))
	else:
		tmp = x - (t * (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 4.4e-60)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	else
		tmp = Float64(x - Float64(t * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 4.4e-60)
		tmp = x / (1.0 + (a * b));
	else
		tmp = x - (t * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 4.4e-60], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.3999999999999998e-60

   1. Initial program 95.7%

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

   3. Taylor expanded in b around inf 58.3%

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

      1. mul-1-neg 58.3%

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

      2. distribute-rgt-neg-out 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in a around inf 58.3%

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

      1. neg-mul-1 58.3%

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

      2. distribute-rgt-neg-in 58.3%

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

      3. exp-prod 52.2%

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

   8. Simplified 52.2%

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

      1. pow-neg 52.2%

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

      2. un-div-inv 52.2%

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

   10. Applied egg-rr 52.2%

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

   11. Taylor expanded in a around 0 31.6%

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

   if 4.3999999999999998e-60 < x

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf 55.3%

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

      1. mul-1-neg 55.3%

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

      2. distribute-lft-neg-out 55.3%

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

      3. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in y around 0 31.9%

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

      1. mul-1-neg 31.9%

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

      2. unsub-neg 31.9%

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

      3. *-commutative 31.9%

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

   8. Simplified 31.9%

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

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.4 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.5% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.7 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.7e-45) (* x (- 1.0 (* a b))) (* x (* t (- y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.7e-45) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (t * -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.7d-45) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (t * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.7e-45) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (t * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.7e-45:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (t * -y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.7e-45)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(t * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.7e-45)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (t * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.7e-45], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-y)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.69999999999999985e-45

   1. Initial program 94.1%

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

   3. Taylor expanded in b around inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. distribute-rgt-neg-out 55.5%

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

   5. Simplified 55.5%

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

   6. Taylor expanded in a around 0 30.3%

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

      1. neg-mul-1 30.3%

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

      2. unsub-neg 30.3%

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

   8. Simplified 30.3%

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

   if 2.69999999999999985e-45 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. distribute-lft-neg-out 53.6%

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

      3. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in y around 0 21.0%

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

      1. associate-*r* 21.0%

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

      2. mul-1-neg 21.0%

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

      3. cancel-sign-sub-inv 21.0%

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

   8. Simplified 21.0%

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

   9. Taylor expanded in t around inf 31.5%

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

       1. mul-1-neg 31.5%

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

       2. associate-*r* 29.9%

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

       3. distribute-rgt-neg-in 29.9%

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

       4. *-commutative 29.9%

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

       5. associate-*r* 32.5%

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

   11. Simplified 32.5%

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

Alternative 15: 19.4% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.8%

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

3. Taylor expanded in t around inf 60.4%

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

   1. mul-1-neg 60.4%

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

   2. distribute-lft-neg-out 60.4%

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

   3. *-commutative 60.4%

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

5. Simplified 60.4%

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

6. Taylor expanded in y around 0 20.9%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(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))))))