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

Percentage Accurate: 96.6% → 99.5%

Time: 15.7s

Alternatives: 18

Speedup: 0.8×

• 41.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. fma-define 96.9%

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

   2. sub-neg 96.9%

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

   3. log1p-define 99.2%

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

3. Simplified 99.2%

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

Alternative 2: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+158}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7.8e+158)
   (* x (exp (* (- a) (+ z b))))
   (* 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) {
	double tmp;
	if (a <= -7.8e+158) {
		tmp = x * exp((-a * (z + b)));
	} else {
		tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - 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 (a <= (-7.8d+158)) then
        tmp = x * exp((-a * (z + b)))
    else
        tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - 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 (a <= -7.8e+158) {
		tmp = x * Math.exp((-a * (z + b)));
	} else {
		tmp = x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7.8e+158:
		tmp = x * math.exp((-a * (z + b)))
	else:
		tmp = x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7.8e+158)
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	else
		tmp = Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -7.8e+158)
		tmp = x * exp((-a * (z + b)));
	else
		tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7.8e+158], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 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. Split input into 2 regimes

2. if a < -7.8e158

   1. Initial program 76.9%

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

   3. Taylor expanded in y around 0 80.4%

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

      1. sub-neg 80.4%

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

      2. log1p-define 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in z around 0 93.4%

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

      1. associate-*r* 93.4%

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

      2. associate-*r* 93.4%

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

      3. distribute-lft-out 93.4%

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

      4. mul-1-neg 93.4%

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

   8. Simplified 93.4%

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

   if -7.8e158 < a

   1. Initial program 98.7%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+158}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+70}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+90}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7.8e+70)
   (* x (exp (* (- a) (+ z b))))
   (if (<= a 3.1e+90)
     (* 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 (a <= -7.8e+70) {
		tmp = x * exp((-a * (z + b)));
	} else if (a <= 3.1e+90) {
		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 (a <= -7.8e+70) {
		tmp = x * Math.exp((-a * (z + b)));
	} else if (a <= 3.1e+90) {
		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 a <= -7.8e+70:
		tmp = x * math.exp((-a * (z + b)))
	elif a <= 3.1e+90:
		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 (a <= -7.8e+70)
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	elseif (a <= 3.1e+90)
		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[LessEqual[a, -7.8e+70], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+90], 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 3 regimes

2. if a < -7.79999999999999949e70

   1. Initial program 85.3%

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

   3. Taylor expanded in y around 0 79.1%

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

      1. sub-neg 79.1%

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

      2. log1p-define 87.4%

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

   5. Simplified 87.4%

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

   6. Taylor expanded in z around 0 87.4%

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

      1. associate-*r* 87.4%

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

      2. associate-*r* 87.4%

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

      3. distribute-lft-out 87.4%

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

      4. mul-1-neg 87.4%

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

   8. Simplified 87.4%

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

   if -7.79999999999999949e70 < a < 3.09999999999999988e90

   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 89.2%

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

   if 3.09999999999999988e90 < a

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 73.5%

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

      1. sub-neg 73.5%

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

      2. log1p-define 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+70}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+90}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+70} \lor \neg \left(a \leq 6.1 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -5.5e+70) (not (<= a 6.1e+94)))
   (* x (exp (* (- a) (+ 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 <= -5.5e+70) || !(a <= 6.1e+94)) {
		tmp = x * exp((-a * (z + 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 <= (-5.5d+70)) .or. (.not. (a <= 6.1d+94))) then
        tmp = x * exp((-a * (z + 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 <= -5.5e+70) || !(a <= 6.1e+94)) {
		tmp = x * Math.exp((-a * (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 <= -5.5e+70) or not (a <= 6.1e+94):
		tmp = x * math.exp((-a * (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 <= -5.5e+70) || !(a <= 6.1e+94))
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + 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 <= -5.5e+70) || ~((a <= 6.1e+94)))
		tmp = x * exp((-a * (z + 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, -5.5e+70], N[Not[LessEqual[a, 6.1e+94]], $MachinePrecision]], N[(x * N[Exp[N[((-a) * N[(z + 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 < -5.49999999999999986e70 or 6.10000000000000035e94 < a

   1. Initial program 89.6%

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

   3. Taylor expanded in y around 0 76.3%

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

      1. sub-neg 76.3%

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

      2. log1p-define 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in z around 0 83.5%

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

      1. associate-*r* 83.5%

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

      2. associate-*r* 83.5%

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

      3. distribute-lft-out 83.5%

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

      4. mul-1-neg 83.5%

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

   8. Simplified 83.5%

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

   if -5.49999999999999986e70 < a < 6.10000000000000035e94

   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 89.2%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+70} \lor \neg \left(a \leq 6.1 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.92 \lor \neg \left(y \leq 2.7 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.92) (not (<= y 2.7e-12)))
   (* x (pow z y))
   (* x (exp (* (- a) (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.92) || !(y <= 2.7e-12)) {
		tmp = x * pow(z, y);
	} 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 <= (-1.92d0)) .or. (.not. (y <= 2.7d-12))) then
        tmp = x * (z ** y)
    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 <= -1.92) || !(y <= 2.7e-12)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((-a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.92) or not (y <= 2.7e-12):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((-a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.92) || !(y <= 2.7e-12))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(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 <= -1.92) || ~((y <= 2.7e-12)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((-a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.92], N[Not[LessEqual[y, 2.7e-12]], $MachinePrecision]], N[(x * N[Power[z, y], $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 < -1.9199999999999999 or 2.6999999999999998e-12 < y

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 86.0%

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

   4. Taylor expanded in t around 0 73.3%

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

   if -1.9199999999999999 < y < 2.6999999999999998e-12

   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. Add Preprocessing

   3. Taylor expanded in y around 0 84.4%

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

      1. sub-neg 84.4%

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

      2. log1p-define 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in z around 0 86.6%

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

      1. associate-*r* 86.6%

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

      2. associate-*r* 86.6%

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

      3. distribute-lft-out 86.6%

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

      4. mul-1-neg 86.6%

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

   8. Simplified 86.6%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.92 \lor \neg \left(y \leq 2.7 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \lor \neg \left(y \leq 2.7 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.1) (not (<= y 2.7e-12)))
   (* 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 <= -1.1) || !(y <= 2.7e-12)) {
		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 <= (-1.1d0)) .or. (.not. (y <= 2.7d-12))) 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 <= -1.1) || !(y <= 2.7e-12)) {
		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 <= -1.1) or not (y <= 2.7e-12):
		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 <= -1.1) || !(y <= 2.7e-12))
		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 <= -1.1) || ~((y <= 2.7e-12)))
		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, -1.1], N[Not[LessEqual[y, 2.7e-12]], $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 < -1.1000000000000001 or 2.6999999999999998e-12 < y

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 86.0%

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

   4. Taylor expanded in t around 0 73.3%

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

   if -1.1000000000000001 < y < 2.6999999999999998e-12

   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. Add Preprocessing

   3. Taylor expanded in b around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. distribute-rgt-neg-out 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \lor \neg \left(y \leq 2.7 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-18} \lor \neg \left(y \leq 3.8 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4e-18) (not (<= y 3.8e-13)))
   (* x (pow z y))
   (* x (- 1.0 (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e-18) || !(y <= 3.8e-13)) {
		tmp = x * pow(z, y);
	} 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) :: tmp
    if ((y <= (-4d-18)) .or. (.not. (y <= 3.8d-13))) then
        tmp = x * (z ** y)
    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 tmp;
	if ((y <= -4e-18) || !(y <= 3.8e-13)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4e-18) or not (y <= 3.8e-13):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * (1.0 - (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4e-18) || !(y <= 3.8e-13))
		tmp = Float64(x * (z ^ y));
	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)
	tmp = 0.0;
	if ((y <= -4e-18) || ~((y <= 3.8e-13)))
		tmp = x * (z ^ y);
	else
		tmp = x * (1.0 - (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4e-18], N[Not[LessEqual[y, 3.8e-13]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0000000000000003e-18 or 3.8e-13 < y

   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. Add Preprocessing

   3. Taylor expanded in y around inf 86.1%

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

   4. Taylor expanded in t around 0 72.7%

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

   if -4.0000000000000003e-18 < y < 3.8e-13

   1. Initial program 97.6%

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

   3. Taylor expanded in b around inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. distribute-rgt-neg-out 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in a around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. unsub-neg 50.6%

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

   8. Simplified 50.6%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-18} \lor \neg \left(y \leq 3.8 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.0% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+203}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-8}:\\ \;\;\;\;a \cdot \left(b \cdot \left(\frac{x}{a \cdot b} - x\right)\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-76}:\\ \;\;\;\;z \cdot \left(\frac{x}{z} - x \cdot a\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-217}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 0.0006:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+238}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9e+203)
   (- x (* x (* y t)))
   (if (<= y -2.2e-8)
     (* a (* b (- (/ x (* a b)) x)))
     (if (<= y -5.5e-76)
       (* z (- (/ x z) (* x a)))
       (if (<= y -1.2e-217)
         (* a (/ x a))
         (if (<= y 0.0006)
           (* x (- 1.0 (* a b)))
           (if (<= y 1.02e+188)
             (* x (* a (- b)))
             (if (<= y 2.1e+238)
               (* y (- (/ x y) (* x t)))
               (* x (* z (- a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9e+203) {
		tmp = x - (x * (y * t));
	} else if (y <= -2.2e-8) {
		tmp = a * (b * ((x / (a * b)) - x));
	} else if (y <= -5.5e-76) {
		tmp = z * ((x / z) - (x * a));
	} else if (y <= -1.2e-217) {
		tmp = a * (x / a);
	} else if (y <= 0.0006) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 1.02e+188) {
		tmp = x * (a * -b);
	} else if (y <= 2.1e+238) {
		tmp = y * ((x / y) - (x * t));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9d+203)) then
        tmp = x - (x * (y * t))
    else if (y <= (-2.2d-8)) then
        tmp = a * (b * ((x / (a * b)) - x))
    else if (y <= (-5.5d-76)) then
        tmp = z * ((x / z) - (x * a))
    else if (y <= (-1.2d-217)) then
        tmp = a * (x / a)
    else if (y <= 0.0006d0) then
        tmp = x * (1.0d0 - (a * b))
    else if (y <= 1.02d+188) then
        tmp = x * (a * -b)
    else if (y <= 2.1d+238) then
        tmp = y * ((x / y) - (x * t))
    else
        tmp = x * (z * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9e+203) {
		tmp = x - (x * (y * t));
	} else if (y <= -2.2e-8) {
		tmp = a * (b * ((x / (a * b)) - x));
	} else if (y <= -5.5e-76) {
		tmp = z * ((x / z) - (x * a));
	} else if (y <= -1.2e-217) {
		tmp = a * (x / a);
	} else if (y <= 0.0006) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 1.02e+188) {
		tmp = x * (a * -b);
	} else if (y <= 2.1e+238) {
		tmp = y * ((x / y) - (x * t));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9e+203:
		tmp = x - (x * (y * t))
	elif y <= -2.2e-8:
		tmp = a * (b * ((x / (a * b)) - x))
	elif y <= -5.5e-76:
		tmp = z * ((x / z) - (x * a))
	elif y <= -1.2e-217:
		tmp = a * (x / a)
	elif y <= 0.0006:
		tmp = x * (1.0 - (a * b))
	elif y <= 1.02e+188:
		tmp = x * (a * -b)
	elif y <= 2.1e+238:
		tmp = y * ((x / y) - (x * t))
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9e+203)
		tmp = Float64(x - Float64(x * Float64(y * t)));
	elseif (y <= -2.2e-8)
		tmp = Float64(a * Float64(b * Float64(Float64(x / Float64(a * b)) - x)));
	elseif (y <= -5.5e-76)
		tmp = Float64(z * Float64(Float64(x / z) - Float64(x * a)));
	elseif (y <= -1.2e-217)
		tmp = Float64(a * Float64(x / a));
	elseif (y <= 0.0006)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (y <= 1.02e+188)
		tmp = Float64(x * Float64(a * Float64(-b)));
	elseif (y <= 2.1e+238)
		tmp = Float64(y * Float64(Float64(x / y) - Float64(x * t)));
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9e+203)
		tmp = x - (x * (y * t));
	elseif (y <= -2.2e-8)
		tmp = a * (b * ((x / (a * b)) - x));
	elseif (y <= -5.5e-76)
		tmp = z * ((x / z) - (x * a));
	elseif (y <= -1.2e-217)
		tmp = a * (x / a);
	elseif (y <= 0.0006)
		tmp = x * (1.0 - (a * b));
	elseif (y <= 1.02e+188)
		tmp = x * (a * -b);
	elseif (y <= 2.1e+238)
		tmp = y * ((x / y) - (x * t));
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9e+203], N[(x - N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.2e-8], N[(a * N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.5e-76], N[(z * N[(N[(x / z), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-217], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0006], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+188], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+238], N[(y * N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -9.0000000000000006e203

   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 79.6%

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

      1. mul-1-neg 79.6%

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

      2. distribute-lft-neg-out 79.6%

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

      3. *-commutative 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in y around 0 39.0%

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

      1. associate-*r* 39.0%

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

      2. mul-1-neg 39.0%

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

      3. *-commutative 39.0%

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

   8. Simplified 39.0%

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

      1. add-sqr-sqrt 0.7%

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

      2. sqrt-unprod 0.8%

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

      3. sqr-neg 0.8%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 9.2%

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

      6. cancel-sign-sub 9.2%

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

      7. associate-*r* 9.1%

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

      8. *-commutative 9.1%

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

      9. add-sqr-sqrt 9.1%

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

      10. sqrt-unprod 55.4%

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

      11. sqr-neg 55.4%

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

      12. sqrt-unprod 46.4%

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

      13. add-sqr-sqrt 47.1%

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

   10. Applied egg-rr 47.1%

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

   if -9.0000000000000006e203 < y < -2.1999999999999998e-8

   1. Initial program 92.5%

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

   3. Taylor expanded in b around inf 45.0%

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

      1. mul-1-neg 45.0%

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

      2. distribute-rgt-neg-out 45.0%

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

   5. Simplified 45.0%

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

   6. Taylor expanded in a around 0 15.6%

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

      1. mul-1-neg 15.6%

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

      2. unsub-neg 15.6%

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

   8. Simplified 15.6%

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

   9. Taylor expanded in a around inf 25.1%

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

   10. Taylor expanded in b around inf 37.3%

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

   if -2.1999999999999998e-8 < y < -5.50000000000000014e-76

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 74.1%

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

      1. sub-neg 74.1%

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

      2. log1p-define 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in b around 0 22.8%

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

   7. Taylor expanded in z around 0 22.8%

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

      1. mul-1-neg 22.8%

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

      2. unsub-neg 22.8%

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

      3. *-commutative 22.8%

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

   9. Simplified 22.8%

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

   10. Taylor expanded in z around inf 43.7%

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

       1. *-commutative 43.7%

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

   12. Simplified 43.7%

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

   if -5.50000000000000014e-76 < y < -1.1999999999999999e-217

   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 75.8%

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

      1. mul-1-neg 75.8%

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

      2. distribute-rgt-neg-out 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in a around 0 37.1%

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

      1. mul-1-neg 37.1%

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

      2. unsub-neg 37.1%

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

   8. Simplified 37.1%

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

   9. Taylor expanded in a around inf 41.7%

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

   10. Taylor expanded in a around 0 49.9%

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

   if -1.1999999999999999e-217 < y < 5.99999999999999947e-4

   1. Initial program 96.8%

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

   3. Taylor expanded in b around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. distribute-rgt-neg-out 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in a around 0 57.7%

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

      1. mul-1-neg 57.7%

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

      2. unsub-neg 57.7%

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

   8. Simplified 57.7%

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

   if 5.99999999999999947e-4 < y < 1.02e188

   1. Initial program 93.1%

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

   3. Taylor expanded in b around inf 28.2%

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

      1. mul-1-neg 28.2%

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

      2. distribute-rgt-neg-out 28.2%

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

   5. Simplified 28.2%

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

   6. Taylor expanded in a around 0 10.3%

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

      1. mul-1-neg 10.3%

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

      2. unsub-neg 10.3%

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

   8. Simplified 10.3%

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

   9. Taylor expanded in a around inf 27.8%

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

       1. neg-mul-1 27.8%

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

       2. distribute-rgt-neg-in 27.8%

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

       3. distribute-rgt-neg-in 27.8%

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

   11. Simplified 27.8%

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

   12. Taylor expanded in a around 0 27.8%

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

       1. mul-1-neg 27.8%

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

       2. associate-*r* 34.3%

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

       3. *-commutative 34.3%

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

       4. distribute-rgt-neg-in 34.3%

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

       5. distribute-rgt-neg-in 34.3%

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

   14. Simplified 34.3%

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

   if 1.02e188 < y < 2.10000000000000007e238

   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 60.9%

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

      1. mul-1-neg 60.9%

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

      2. distribute-lft-neg-out 60.9%

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

      3. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   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. associate-*r* 31.9%

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

      2. mul-1-neg 31.9%

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

      3. *-commutative 31.9%

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

   8. Simplified 31.9%

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

   9. Taylor expanded in y around inf 50.9%

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

       1. +-commutative 50.9%

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

       2. mul-1-neg 50.9%

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

       3. unsub-neg 50.9%

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

       4. *-commutative 50.9%

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

   11. Simplified 50.9%

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

   if 2.10000000000000007e238 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 43.1%

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

      1. sub-neg 43.1%

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

      2. log1p-define 43.1%

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

   5. Simplified 43.1%

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

   6. Taylor expanded in b around 0 3.0%

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

   7. Taylor expanded in z around 0 2.5%

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

      1. mul-1-neg 2.5%

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

      2. unsub-neg 2.5%

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

      3. *-commutative 2.5%

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

   9. Simplified 2.5%

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

   10. Taylor expanded in a around inf 20.3%

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

       1. mul-1-neg 20.3%

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

       2. *-commutative 20.3%

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

       3. associate-*r* 35.2%

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

       4. distribute-rgt-neg-in 35.2%

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

       5. distribute-rgt-neg-in 35.2%

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

   12. Simplified 35.2%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(-a\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+203}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-8}:\\ \;\;\;\;a \cdot \left(b \cdot \left(\frac{x}{a \cdot b} - x\right)\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-76}:\\ \;\;\;\;z \cdot \left(\frac{x}{z} - x \cdot a\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-217}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 0.0006:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+238}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 33.9% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 0.00033:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+181}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+238}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.25e-84)
   (* t (- (/ x t) (* x y)))
   (if (<= y 0.00033)
     (* x (- 1.0 (* a b)))
     (if (<= y 2.7e+181)
       (* x (* a (- b)))
       (if (<= y 7.2e+238) (* y (- (/ x y) (* x t))) (* x (* z (- a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.25e-84) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 0.00033) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 2.7e+181) {
		tmp = x * (a * -b);
	} else if (y <= 7.2e+238) {
		tmp = y * ((x / y) - (x * t));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.25d-84)) then
        tmp = t * ((x / t) - (x * y))
    else if (y <= 0.00033d0) then
        tmp = x * (1.0d0 - (a * b))
    else if (y <= 2.7d+181) then
        tmp = x * (a * -b)
    else if (y <= 7.2d+238) then
        tmp = y * ((x / y) - (x * t))
    else
        tmp = x * (z * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.25e-84) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 0.00033) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 2.7e+181) {
		tmp = x * (a * -b);
	} else if (y <= 7.2e+238) {
		tmp = y * ((x / y) - (x * t));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.25e-84:
		tmp = t * ((x / t) - (x * y))
	elif y <= 0.00033:
		tmp = x * (1.0 - (a * b))
	elif y <= 2.7e+181:
		tmp = x * (a * -b)
	elif y <= 7.2e+238:
		tmp = y * ((x / y) - (x * t))
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.25e-84)
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	elseif (y <= 0.00033)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (y <= 2.7e+181)
		tmp = Float64(x * Float64(a * Float64(-b)));
	elseif (y <= 7.2e+238)
		tmp = Float64(y * Float64(Float64(x / y) - Float64(x * t)));
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.25e-84)
		tmp = t * ((x / t) - (x * y));
	elseif (y <= 0.00033)
		tmp = x * (1.0 - (a * b));
	elseif (y <= 2.7e+181)
		tmp = x * (a * -b);
	elseif (y <= 7.2e+238)
		tmp = y * ((x / y) - (x * t));
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.25e-84], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00033], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+181], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+238], N[(y * N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.25000000000000008e-84

   1. Initial program 95.0%

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

   3. Taylor expanded in t around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. distribute-lft-neg-out 55.7%

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

      3. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in y around 0 30.4%

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

      1. associate-*r* 30.4%

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

      2. mul-1-neg 30.4%

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

      3. *-commutative 30.4%

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

   8. Simplified 30.4%

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

   9. Taylor expanded in t around inf 33.0%

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

       1. +-commutative 33.0%

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

       2. mul-1-neg 33.0%

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

       3. unsub-neg 33.0%

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

   11. Simplified 33.0%

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

   if -2.25000000000000008e-84 < y < 3.3e-4

   1. Initial program 97.3%

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

   3. Taylor expanded in b around inf 83.0%

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

      1. mul-1-neg 83.0%

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

      2. distribute-rgt-neg-out 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in a around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. unsub-neg 54.1%

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

   8. Simplified 54.1%

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

   if 3.3e-4 < y < 2.70000000000000007e181

   1. Initial program 93.1%

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

   3. Taylor expanded in b around inf 28.2%

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

      1. mul-1-neg 28.2%

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

      2. distribute-rgt-neg-out 28.2%

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

   5. Simplified 28.2%

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

   6. Taylor expanded in a around 0 10.3%

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

      1. mul-1-neg 10.3%

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

      2. unsub-neg 10.3%

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

   8. Simplified 10.3%

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

   9. Taylor expanded in a around inf 27.8%

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

       1. neg-mul-1 27.8%

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

       2. distribute-rgt-neg-in 27.8%

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

       3. distribute-rgt-neg-in 27.8%

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

   11. Simplified 27.8%

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

   12. Taylor expanded in a around 0 27.8%

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

       1. mul-1-neg 27.8%

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

       2. associate-*r* 34.3%

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

       3. *-commutative 34.3%

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

       4. distribute-rgt-neg-in 34.3%

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

       5. distribute-rgt-neg-in 34.3%

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

   14. Simplified 34.3%

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

   if 2.70000000000000007e181 < y < 7.19999999999999942e238

   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 60.9%

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

      1. mul-1-neg 60.9%

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

      2. distribute-lft-neg-out 60.9%

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

      3. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   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. associate-*r* 31.9%

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

      2. mul-1-neg 31.9%

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

      3. *-commutative 31.9%

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

   8. Simplified 31.9%

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

   9. Taylor expanded in y around inf 50.9%

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

       1. +-commutative 50.9%

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

       2. mul-1-neg 50.9%

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

       3. unsub-neg 50.9%

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

       4. *-commutative 50.9%

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

   11. Simplified 50.9%

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

   if 7.19999999999999942e238 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 43.1%

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

      1. sub-neg 43.1%

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

      2. log1p-define 43.1%

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

   5. Simplified 43.1%

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

   6. Taylor expanded in b around 0 3.0%

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

   7. Taylor expanded in z around 0 2.5%

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

      1. mul-1-neg 2.5%

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

      2. unsub-neg 2.5%

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

      3. *-commutative 2.5%

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

   9. Simplified 2.5%

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

   10. Taylor expanded in a around inf 20.3%

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

       1. mul-1-neg 20.3%

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

       2. *-commutative 20.3%

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

       3. associate-*r* 35.2%

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

       4. distribute-rgt-neg-in 35.2%

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

       5. distribute-rgt-neg-in 35.2%

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

   12. Simplified 35.2%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(-a\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 10: 34.3% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.2e-83)
   (* t (- (/ x t) (* x y)))
   (if (<= y 9e-10) (* x (- 1.0 (* a b))) (* x (* z (- a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.2e-83) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 9e-10) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.2d-83)) then
        tmp = t * ((x / t) - (x * y))
    else if (y <= 9d-10) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (z * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.2e-83) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 9e-10) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.2e-83:
		tmp = t * ((x / t) - (x * y))
	elif y <= 9e-10:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.2e-83)
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	elseif (y <= 9e-10)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.2e-83)
		tmp = t * ((x / t) - (x * y));
	elseif (y <= 9e-10)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.2e-83], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-10], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.19999999999999985e-83

   1. Initial program 95.0%

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

   3. Taylor expanded in t around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. distribute-lft-neg-out 55.7%

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

      3. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in y around 0 30.4%

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

      1. associate-*r* 30.4%

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

      2. mul-1-neg 30.4%

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

      3. *-commutative 30.4%

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

   8. Simplified 30.4%

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

   9. Taylor expanded in t around inf 33.0%

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

       1. +-commutative 33.0%

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

       2. mul-1-neg 33.0%

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

       3. unsub-neg 33.0%

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

   11. Simplified 33.0%

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

   if -6.19999999999999985e-83 < y < 8.9999999999999999e-10

   1. Initial program 97.3%

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

   3. Taylor expanded in b around inf 83.0%

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

      1. mul-1-neg 83.0%

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

      2. distribute-rgt-neg-out 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in a around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. unsub-neg 54.1%

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

   8. Simplified 54.1%

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

   if 8.9999999999999999e-10 < y

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 0 33.1%

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

      1. sub-neg 33.1%

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

      2. log1p-define 36.1%

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

   5. Simplified 36.1%

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

   6. Taylor expanded in b around 0 5.2%

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

   7. Taylor expanded in z around 0 6.4%

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

      1. mul-1-neg 6.4%

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

      2. unsub-neg 6.4%

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

      3. *-commutative 6.4%

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

   9. Simplified 6.4%

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

   10. Taylor expanded in a around inf 27.2%

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

       1. mul-1-neg 27.2%

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

       2. *-commutative 27.2%

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

       3. associate-*r* 28.4%

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

       4. distribute-rgt-neg-in 28.4%

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

       5. distribute-rgt-neg-in 28.4%

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

   12. Simplified 28.4%

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

Alternative 11: 32.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-208}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1e-208)
   (- x (* x (* y t)))
   (if (<= y 7.2e-9) (* x (- 1.0 (* a b))) (* x (* z (- a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1e-208) {
		tmp = x - (x * (y * t));
	} else if (y <= 7.2e-9) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1d-208)) then
        tmp = x - (x * (y * t))
    else if (y <= 7.2d-9) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (z * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1e-208) {
		tmp = x - (x * (y * t));
	} else if (y <= 7.2e-9) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1e-208:
		tmp = x - (x * (y * t))
	elif y <= 7.2e-9:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1e-208)
		tmp = Float64(x - Float64(x * Float64(y * t)));
	elseif (y <= 7.2e-9)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1e-208)
		tmp = x - (x * (y * t));
	elseif (y <= 7.2e-9)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1e-208], N[(x - N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-9], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0000000000000001e-208

   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 57.0%

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

      1. mul-1-neg 57.0%

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

      2. distribute-lft-neg-out 57.0%

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

      3. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in y around 0 31.0%

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

      1. associate-*r* 31.0%

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

      2. mul-1-neg 31.0%

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

      3. *-commutative 31.0%

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

   8. Simplified 31.0%

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

      1. add-sqr-sqrt 7.2%

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

      2. sqrt-unprod 9.8%

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

      3. sqr-neg 9.8%

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

      4. sqrt-unprod 2.7%

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

      5. add-sqr-sqrt 15.2%

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

      6. cancel-sign-sub 15.2%

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

      7. associate-*r* 14.1%

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

      8. *-commutative 14.1%

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

      9. add-sqr-sqrt 11.5%

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

      10. sqrt-unprod 41.2%

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

      11. sqr-neg 41.2%

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

      12. sqrt-unprod 25.8%

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

      13. add-sqr-sqrt 33.0%

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

   10. Applied egg-rr 33.0%

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

   if -1.0000000000000001e-208 < y < 7.2e-9

   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. Add Preprocessing

   3. Taylor expanded in b around inf 85.2%

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

      1. mul-1-neg 85.2%

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

      2. distribute-rgt-neg-out 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in a around 0 57.6%

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

      1. mul-1-neg 57.6%

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

      2. unsub-neg 57.6%

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

   8. Simplified 57.6%

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

   if 7.2e-9 < y

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 0 33.1%

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

      1. sub-neg 33.1%

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

      2. log1p-define 36.1%

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

   5. Simplified 36.1%

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

   6. Taylor expanded in b around 0 5.2%

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

   7. Taylor expanded in z around 0 6.4%

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

      1. mul-1-neg 6.4%

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

      2. unsub-neg 6.4%

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

      3. *-commutative 6.4%

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

   9. Simplified 6.4%

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

   10. Taylor expanded in a around inf 27.2%

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

       1. mul-1-neg 27.2%

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

       2. *-commutative 27.2%

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

       3. associate-*r* 28.4%

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

       4. distribute-rgt-neg-in 28.4%

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

       5. distribute-rgt-neg-in 28.4%

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

   12. Simplified 28.4%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-208}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 33.1% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+78}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.6e+78)
   (* a (/ x a))
   (if (<= y 2.7e-11) (* x (- 1.0 (* a b))) (* x (* z (- a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e+78) {
		tmp = a * (x / a);
	} else if (y <= 2.7e-11) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.6d+78)) then
        tmp = a * (x / a)
    else if (y <= 2.7d-11) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (z * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e+78) {
		tmp = a * (x / a);
	} else if (y <= 2.7e-11) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.6e+78:
		tmp = a * (x / a)
	elif y <= 2.7e-11:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.6e+78)
		tmp = Float64(a * Float64(x / a));
	elseif (y <= 2.7e-11)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.6e+78)
		tmp = a * (x / a);
	elseif (y <= 2.7e-11)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.6e+78], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-11], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999997e78

   1. Initial program 93.8%

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

   3. Taylor expanded in b around inf 35.1%

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

      1. mul-1-neg 35.1%

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

      2. distribute-rgt-neg-out 35.1%

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

   5. Simplified 35.1%

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

   6. Taylor expanded in a around 0 12.7%

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

      1. mul-1-neg 12.7%

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

      2. unsub-neg 12.7%

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

   8. Simplified 12.7%

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

   9. Taylor expanded in a around inf 20.6%

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

   10. Taylor expanded in a around 0 21.2%

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

   if -1.59999999999999997e78 < y < 2.70000000000000005e-11

   1. Initial program 97.2%

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

   3. Taylor expanded in b around inf 79.6%

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

      1. mul-1-neg 79.6%

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

      2. distribute-rgt-neg-out 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in a around 0 48.6%

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

      1. mul-1-neg 48.6%

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

      2. unsub-neg 48.6%

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

   8. Simplified 48.6%

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

   if 2.70000000000000005e-11 < y

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 0 33.1%

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

      1. sub-neg 33.1%

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

      2. log1p-define 36.1%

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

   5. Simplified 36.1%

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

   6. Taylor expanded in b around 0 5.2%

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

   7. Taylor expanded in z around 0 6.4%

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

      1. mul-1-neg 6.4%

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

      2. unsub-neg 6.4%

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

      3. *-commutative 6.4%

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

   9. Simplified 6.4%

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

   10. Taylor expanded in a around inf 27.2%

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

       1. mul-1-neg 27.2%

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

       2. *-commutative 27.2%

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

       3. associate-*r* 28.4%

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

       4. distribute-rgt-neg-in 28.4%

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

       5. distribute-rgt-neg-in 28.4%

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

   12. Simplified 28.4%

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

Alternative 13: 28.5% accurate, 28.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.6 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 9.6e-25) (* a (/ x a)) (* x (* z (- a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 9.6e-25) {
		tmp = a * (x / a);
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 9.6d-25) then
        tmp = a * (x / a)
    else
        tmp = x * (z * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 9.6e-25) {
		tmp = a * (x / a);
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 9.6e-25:
		tmp = a * (x / a)
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 9.6e-25)
		tmp = Float64(a * Float64(x / a));
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 9.6e-25)
		tmp = a * (x / a);
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 9.6e-25], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.60000000000000037e-25

   1. Initial program 96.3%

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

   3. Taylor expanded in b around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-rgt-neg-out 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in a around 0 38.1%

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

      1. mul-1-neg 38.1%

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

      2. unsub-neg 38.1%

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

   8. Simplified 38.1%

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

   9. Taylor expanded in a around inf 37.5%

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

   10. Taylor expanded in a around 0 34.6%

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

   if 9.60000000000000037e-25 < y

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0 34.5%

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

      1. sub-neg 34.5%

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

      2. log1p-define 37.5%

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

   5. Simplified 37.5%

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

   6. Taylor expanded in b around 0 6.1%

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

   7. Taylor expanded in z around 0 8.6%

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

      1. mul-1-neg 8.6%

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

      2. unsub-neg 8.6%

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

      3. *-commutative 8.6%

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

   9. Simplified 8.6%

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

   10. Taylor expanded in a around inf 27.9%

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

       1. mul-1-neg 27.9%

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

       2. *-commutative 27.9%

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

       3. associate-*r* 29.2%

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

       4. distribute-rgt-neg-in 29.2%

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

       5. distribute-rgt-neg-in 29.2%

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

   12. Simplified 29.2%

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

Alternative 14: 27.9% accurate, 28.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.8 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 7.8e-25) (* a (/ x a)) (* x (* a (- b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 7.8e-25) {
		tmp = a * (x / a);
	} else {
		tmp = x * (a * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 7.8d-25) then
        tmp = a * (x / a)
    else
        tmp = x * (a * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 7.8e-25) {
		tmp = a * (x / a);
	} else {
		tmp = x * (a * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 7.8e-25:
		tmp = a * (x / a)
	else:
		tmp = x * (a * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 7.8e-25)
		tmp = Float64(a * Float64(x / a));
	else
		tmp = Float64(x * Float64(a * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 7.8e-25)
		tmp = a * (x / a);
	else
		tmp = x * (a * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 7.8e-25], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.8e-25

   1. Initial program 96.3%

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

   3. Taylor expanded in b around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-rgt-neg-out 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in a around 0 38.1%

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

      1. mul-1-neg 38.1%

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

      2. unsub-neg 38.1%

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

   8. Simplified 38.1%

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

   9. Taylor expanded in a around inf 37.5%

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

   10. Taylor expanded in a around 0 34.6%

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

   if 7.8e-25 < y

   1. Initial program 95.6%

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

   3. Taylor expanded in b around inf 33.1%

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

      1. mul-1-neg 33.1%

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

      2. distribute-rgt-neg-out 33.1%

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

   5. Simplified 33.1%

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

   6. Taylor expanded in a around 0 9.9%

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

      1. mul-1-neg 9.9%

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

      2. unsub-neg 9.9%

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

   8. Simplified 9.9%

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

   9. Taylor expanded in a around inf 23.1%

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

       1. neg-mul-1 23.1%

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

       2. distribute-rgt-neg-in 23.1%

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

       3. distribute-rgt-neg-in 23.1%

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

   11. Simplified 23.1%

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

   12. Taylor expanded in a around 0 23.1%

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

       1. mul-1-neg 23.1%

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

       2. associate-*r* 27.3%

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

       3. *-commutative 27.3%

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

       4. distribute-rgt-neg-in 27.3%

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

       5. distribute-rgt-neg-in 27.3%

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

   14. Simplified 27.3%

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

Alternative 15: 27.7% accurate, 28.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.4 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 5.4e-25) (* a (/ x a)) (* a (* x (- b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 5.4e-25) {
		tmp = a * (x / a);
	} 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 <= 5.4d-25) then
        tmp = a * (x / a)
    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 <= 5.4e-25) {
		tmp = a * (x / a);
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 5.4e-25:
		tmp = a * (x / a)
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 5.4e-25)
		tmp = Float64(a * Float64(x / a));
	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 <= 5.4e-25)
		tmp = a * (x / a);
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 5.4e-25], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.40000000000000032e-25

   1. Initial program 96.3%

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

   3. Taylor expanded in b around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-rgt-neg-out 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in a around 0 38.1%

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

      1. mul-1-neg 38.1%

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

      2. unsub-neg 38.1%

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

   8. Simplified 38.1%

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

   9. Taylor expanded in a around inf 37.5%

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

   10. Taylor expanded in a around 0 34.6%

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

   if 5.40000000000000032e-25 < y

   1. Initial program 95.6%

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

   3. Taylor expanded in b around inf 33.1%

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

      1. mul-1-neg 33.1%

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

      2. distribute-rgt-neg-out 33.1%

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

   5. Simplified 33.1%

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

   6. Taylor expanded in a around 0 9.9%

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

      1. mul-1-neg 9.9%

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

      2. unsub-neg 9.9%

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

   8. Simplified 9.9%

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

   9. Taylor expanded in a around inf 23.1%

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

       1. neg-mul-1 23.1%

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

       2. distribute-rgt-neg-in 23.1%

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

       3. distribute-rgt-neg-in 23.1%

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

   11. Simplified 23.1%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.4 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 26.1% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.15e+66) (* a (/ x a)) (* a (* x b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.15e+66) {
		tmp = a * (x / a);
	} 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 <= 1.15d+66) then
        tmp = a * (x / a)
    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 <= 1.15e+66) {
		tmp = a * (x / a);
	} else {
		tmp = a * (x * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.15e+66:
		tmp = a * (x / a)
	else:
		tmp = a * (x * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.15e+66)
		tmp = Float64(a * Float64(x / a));
	else
		tmp = Float64(a * Float64(x * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.15e+66)
		tmp = a * (x / a);
	else
		tmp = a * (x * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.15e+66], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.15e66

   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 65.8%

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

      1. mul-1-neg 65.8%

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

      2. distribute-rgt-neg-out 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in a around 0 36.8%

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

      1. mul-1-neg 36.8%

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

      2. unsub-neg 36.8%

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

   8. Simplified 36.8%

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

   9. Taylor expanded in a around inf 37.2%

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

   10. Taylor expanded in a around 0 33.6%

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

   if 1.15e66 < y

   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. Add Preprocessing

   3. Taylor expanded in b around inf 30.9%

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

      1. mul-1-neg 30.9%

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

      2. distribute-rgt-neg-out 30.9%

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

   5. Simplified 30.9%

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

   6. Taylor expanded in a around 0 5.1%

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

      1. mul-1-neg 5.1%

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

      2. unsub-neg 5.1%

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

   8. Simplified 5.1%

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

   9. Taylor expanded in a around inf 20.6%

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

       1. neg-mul-1 20.6%

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

       2. distribute-rgt-neg-in 20.6%

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

       3. distribute-rgt-neg-in 20.6%

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

   11. Simplified 20.6%

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

       1. pow1 20.6%

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

       2. associate-*r* 24.3%

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

       3. *-commutative 24.3%

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

       4. add-sqr-sqrt 15.0%

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

       5. sqrt-unprod 25.9%

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

       6. sqr-neg 25.9%

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

       7. sqrt-unprod 9.3%

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

       8. add-sqr-sqrt 20.6%

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

   13. Applied egg-rr 20.6%

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

       1. unpow1 20.6%

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

       2. *-commutative 20.6%

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

       3. associate-*r* 20.6%

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

       4. *-commutative 20.6%

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

   15. Simplified 20.6%

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

Alternative 17: 23.3% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 1.7e-5) x (* a (* x b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.7e-5) {
		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 (y <= 1.7d-5) 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 (y <= 1.7e-5) {
		tmp = x;
	} else {
		tmp = a * (x * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.7e-5:
		tmp = x
	else:
		tmp = a * (x * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.7e-5)
		tmp = x;
	else
		tmp = Float64(a * Float64(x * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.7e-5)
		tmp = x;
	else
		tmp = a * (x * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.7e-5], x, N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.7e-5

   1. Initial program 96.4%

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

   3. Taylor expanded in b around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. distribute-rgt-neg-out 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in a around 0 27.8%

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

   if 1.7e-5 < y

   1. Initial program 95.5%

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

   3. Taylor expanded in b around inf 31.5%

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

      1. mul-1-neg 31.5%

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

      2. distribute-rgt-neg-out 31.5%

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

   5. Simplified 31.5%

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

   6. Taylor expanded in a around 0 7.7%

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

      1. mul-1-neg 7.7%

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

      2. unsub-neg 7.7%

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

   8. Simplified 7.7%

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

   9. Taylor expanded in a around inf 22.2%

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

       1. neg-mul-1 22.2%

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

       2. distribute-rgt-neg-in 22.2%

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

       3. distribute-rgt-neg-in 22.2%

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

   11. Simplified 22.2%

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

       1. pow1 22.2%

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

       2. associate-*r* 26.5%

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

       3. *-commutative 26.5%

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

       4. add-sqr-sqrt 16.1%

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

       5. sqrt-unprod 24.5%

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

       6. sqr-neg 24.5%

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

       7. sqrt-unprod 8.8%

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

       8. add-sqr-sqrt 20.5%

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

   13. Applied egg-rr 20.5%

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

       1. unpow1 20.5%

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

       2. *-commutative 20.5%

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

       3. associate-*r* 19.1%

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

       4. *-commutative 19.1%

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

   15. Simplified 19.1%

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

Alternative 18: 19.3% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

3. Taylor expanded in b around inf 59.1%

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

   1. mul-1-neg 59.1%

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

   2. distribute-rgt-neg-out 59.1%

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

5. Simplified 59.1%

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

6. Taylor expanded in a around 0 21.7%

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

Reproduce

herbie shell --seed 2024103 
(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))))))