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

Percentage Accurate: 96.7% → 99.7%

Time: 18.6s

Alternatives: 18

Speedup: 0.8×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.7% 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: 99.7% 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 96.7%

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

   1. fma-def 97.4%

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

   2. sub-neg 97.4%

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

   3. log1p-def 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

   1. +-commutative 96.7%

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

   2. fma-def 97.1%

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

   3. sub-neg 97.1%

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

   4. log1p-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 3: 86.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -850000000000 \lor \neg \left(y \leq 1.85 \cdot 10^{-83}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -850000000000.0) (not (<= y 1.85e-83)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (- z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -850000000000.0) || !(y <= 1.85e-83)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * (-z - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-850000000000.0d0)) .or. (.not. (y <= 1.85d-83))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((a * (-z - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -850000000000.0) || !(y <= 1.85e-83)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * (-z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -850000000000.0) or not (y <= 1.85e-83):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * (-z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -850000000000.0) || !(y <= 1.85e-83))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -850000000000.0) || ~((y <= 1.85e-83)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((a * (-z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -850000000000.0], N[Not[LessEqual[y, 1.85e-83]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5e11 or 1.84999999999999997e-83 < y

   1. Initial program 97.8%

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

   2. Taylor expanded in y around inf 88.1%

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

   if -8.5e11 < y < 1.84999999999999997e-83

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0 84.9%

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

      1. sub-neg 84.9%

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

      2. neg-mul-1 84.9%

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

      3. log1p-def 90.4%

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

      4. neg-mul-1 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in z around 0 90.4%

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

      1. neg-mul-1 90.4%

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

      2. +-commutative 90.4%

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

      3. neg-mul-1 90.4%

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

      4. unsub-neg 90.4%

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

   7. Simplified 90.4%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -850000000000 \lor \neg \left(y \leq 1.85 \cdot 10^{-83}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \]

Alternative 4: 87.5% accurate, 1.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.5e+56) {
		tmp = x * exp((y * -t));
	} else {
		tmp = x * exp(((y * log(z)) - (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 (t <= (-6.5d+56)) then
        tmp = x * exp((y * -t))
    else
        tmp = x * exp(((y * log(z)) - (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 (t <= -6.5e+56) {
		tmp = x * Math.exp((y * -t));
	} else {
		tmp = x * Math.exp(((y * Math.log(z)) - (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.5e+56:
		tmp = x * math.exp((y * -t))
	else:
		tmp = x * math.exp(((y * math.log(z)) - (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.5e+56)
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	else
		tmp = Float64(x * exp(Float64(Float64(y * log(z)) - Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6.5e+56)
		tmp = x * exp((y * -t));
	else
		tmp = x * exp(((y * log(z)) - (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if t < -6.5000000000000001e56

   1. Initial program 98.3%

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

   2. Taylor expanded in t around inf 85.2%

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

      1. mul-1-neg 85.2%

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

      2. distribute-rgt-neg-out 85.2%

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

   4. Simplified 85.2%

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

   if -6.5000000000000001e56 < t

   1. Initial program 96.2%

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

      1. +-commutative 96.2%

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

      2. fma-def 96.2%

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

      3. sub-neg 96.2%

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

      4. log1p-def 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around 0 96.2%

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

   5. Taylor expanded in t around 0 91.3%

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

      1. mul-1-neg 91.3%

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

      2. unsub-neg 91.3%

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

   7. Simplified 91.3%

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

4. Final simplification 89.9%

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

Alternative 5: 96.2% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

   1. +-commutative 96.7%

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

   2. fma-def 97.1%

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

   3. sub-neg 97.1%

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

   4. log1p-def 99.2%

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

3. Simplified 99.2%

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

4. Taylor expanded in z around 0 96.7%

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

5. Final simplification 96.7%

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

Alternative 6: 71.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{a \cdot \left(-b\right)}\\ t_2 := x \cdot e^{y \cdot \left(-t\right)}\\ t_3 := x \cdot {z}^{y}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-280}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.14 \cdot 10^{-85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.04 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* a (- b)))))
        (t_2 (* x (exp (* y (- t)))))
        (t_3 (* x (pow z y))))
   (if (<= t -4.5e+108)
     t_2
     (if (<= t -2.1e-106)
       t_1
       (if (<= t 5.2e-280)
         t_3
         (if (<= t 1.56e-237)
           t_1
           (if (<= t 1.14e-85) t_3 (if (<= t 1.04e+30) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((a * -b));
	double t_2 = x * exp((y * -t));
	double t_3 = x * pow(z, y);
	double tmp;
	if (t <= -4.5e+108) {
		tmp = t_2;
	} else if (t <= -2.1e-106) {
		tmp = t_1;
	} else if (t <= 5.2e-280) {
		tmp = t_3;
	} else if (t <= 1.56e-237) {
		tmp = t_1;
	} else if (t <= 1.14e-85) {
		tmp = t_3;
	} else if (t <= 1.04e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * exp((a * -b))
    t_2 = x * exp((y * -t))
    t_3 = x * (z ** y)
    if (t <= (-4.5d+108)) then
        tmp = t_2
    else if (t <= (-2.1d-106)) then
        tmp = t_1
    else if (t <= 5.2d-280) then
        tmp = t_3
    else if (t <= 1.56d-237) then
        tmp = t_1
    else if (t <= 1.14d-85) then
        tmp = t_3
    else if (t <= 1.04d+30) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((a * -b));
	double t_2 = x * Math.exp((y * -t));
	double t_3 = x * Math.pow(z, y);
	double tmp;
	if (t <= -4.5e+108) {
		tmp = t_2;
	} else if (t <= -2.1e-106) {
		tmp = t_1;
	} else if (t <= 5.2e-280) {
		tmp = t_3;
	} else if (t <= 1.56e-237) {
		tmp = t_1;
	} else if (t <= 1.14e-85) {
		tmp = t_3;
	} else if (t <= 1.04e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((a * -b))
	t_2 = x * math.exp((y * -t))
	t_3 = x * math.pow(z, y)
	tmp = 0
	if t <= -4.5e+108:
		tmp = t_2
	elif t <= -2.1e-106:
		tmp = t_1
	elif t <= 5.2e-280:
		tmp = t_3
	elif t <= 1.56e-237:
		tmp = t_1
	elif t <= 1.14e-85:
		tmp = t_3
	elif t <= 1.04e+30:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(a * Float64(-b))))
	t_2 = Float64(x * exp(Float64(y * Float64(-t))))
	t_3 = Float64(x * (z ^ y))
	tmp = 0.0
	if (t <= -4.5e+108)
		tmp = t_2;
	elseif (t <= -2.1e-106)
		tmp = t_1;
	elseif (t <= 5.2e-280)
		tmp = t_3;
	elseif (t <= 1.56e-237)
		tmp = t_1;
	elseif (t <= 1.14e-85)
		tmp = t_3;
	elseif (t <= 1.04e+30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((a * -b));
	t_2 = x * exp((y * -t));
	t_3 = x * (z ^ y);
	tmp = 0.0;
	if (t <= -4.5e+108)
		tmp = t_2;
	elseif (t <= -2.1e-106)
		tmp = t_1;
	elseif (t <= 5.2e-280)
		tmp = t_3;
	elseif (t <= 1.56e-237)
		tmp = t_1;
	elseif (t <= 1.14e-85)
		tmp = t_3;
	elseif (t <= 1.04e+30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+108], t$95$2, If[LessEqual[t, -2.1e-106], t$95$1, If[LessEqual[t, 5.2e-280], t$95$3, If[LessEqual[t, 1.56e-237], t$95$1, If[LessEqual[t, 1.14e-85], t$95$3, If[LessEqual[t, 1.04e+30], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5e108 or 1.04e30 < t

   1. Initial program 96.2%

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

   2. Taylor expanded in t around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. distribute-rgt-neg-out 80.4%

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

   4. Simplified 80.4%

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

   if -4.5e108 < t < -2.10000000000000003e-106 or 5.2e-280 < t < 1.5599999999999999e-237 or 1.1400000000000001e-85 < t < 1.04e30

   1. Initial program 98.8%

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

   2. Taylor expanded in b around inf 82.5%

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

      1. associate-*r* 82.5%

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

      2. *-commutative 82.5%

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

      3. neg-mul-1 82.5%

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

   4. Simplified 82.5%

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

   if -2.10000000000000003e-106 < t < 5.2e-280 or 1.5599999999999999e-237 < t < 1.1400000000000001e-85

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf 75.3%

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

   3. Taylor expanded in t around 0 75.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+108}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-106}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-280}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-237}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;t \leq 1.14 \cdot 10^{-85}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 1.04 \cdot 10^{+30}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 7: 74.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-80}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+52} \lor \neg \left(y \leq 8 \cdot 10^{+126}\right) \land y \leq 2.6 \cdot 10^{+210}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -1.15e+49)
     t_1
     (if (<= y 3.9e-80)
       (* x (exp (* a (- (- z) b))))
       (if (or (<= y 6.6e+52) (and (not (<= y 8e+126)) (<= y 2.6e+210)))
         (* x (exp (* y (- t))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -1.15e+49) {
		tmp = t_1;
	} else if (y <= 3.9e-80) {
		tmp = x * exp((a * (-z - b)));
	} else if ((y <= 6.6e+52) || (!(y <= 8e+126) && (y <= 2.6e+210))) {
		tmp = x * exp((y * -t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-1.15d+49)) then
        tmp = t_1
    else if (y <= 3.9d-80) then
        tmp = x * exp((a * (-z - b)))
    else if ((y <= 6.6d+52) .or. (.not. (y <= 8d+126)) .and. (y <= 2.6d+210)) then
        tmp = x * exp((y * -t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -1.15e+49) {
		tmp = t_1;
	} else if (y <= 3.9e-80) {
		tmp = x * Math.exp((a * (-z - b)));
	} else if ((y <= 6.6e+52) || (!(y <= 8e+126) && (y <= 2.6e+210))) {
		tmp = x * Math.exp((y * -t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -1.15e+49:
		tmp = t_1
	elif y <= 3.9e-80:
		tmp = x * math.exp((a * (-z - b)))
	elif (y <= 6.6e+52) or (not (y <= 8e+126) and (y <= 2.6e+210)):
		tmp = x * math.exp((y * -t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -1.15e+49)
		tmp = t_1;
	elseif (y <= 3.9e-80)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	elseif ((y <= 6.6e+52) || (!(y <= 8e+126) && (y <= 2.6e+210)))
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -1.15e+49)
		tmp = t_1;
	elseif (y <= 3.9e-80)
		tmp = x * exp((a * (-z - b)));
	elseif ((y <= 6.6e+52) || (~((y <= 8e+126)) && (y <= 2.6e+210)))
		tmp = x * exp((y * -t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+49], t$95$1, If[LessEqual[y, 3.9e-80], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 6.6e+52], And[N[Not[LessEqual[y, 8e+126]], $MachinePrecision], LessEqual[y, 2.6e+210]]], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000001e49 or 6.6e52 < y < 7.9999999999999994e126 or 2.5999999999999999e210 < y

   1. Initial program 97.7%

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

   2. Taylor expanded in y around inf 90.9%

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

   3. Taylor expanded in t around 0 70.6%

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

   if -1.15000000000000001e49 < y < 3.8999999999999998e-80

   1. Initial program 95.5%

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

   2. Taylor expanded in y around 0 83.5%

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

      1. sub-neg 83.5%

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

      2. neg-mul-1 83.5%

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

      3. log1p-def 88.6%

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

      4. neg-mul-1 88.6%

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

   4. Simplified 88.6%

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

   5. Taylor expanded in z around 0 88.6%

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

      1. neg-mul-1 88.6%

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

      2. +-commutative 88.6%

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

      3. neg-mul-1 88.6%

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

      4. unsub-neg 88.6%

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

   7. Simplified 88.6%

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

   if 3.8999999999999998e-80 < y < 6.6e52 or 7.9999999999999994e126 < y < 2.5999999999999999e210

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-rgt-neg-out 76.2%

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

   4. Simplified 76.2%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+49}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-80}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+52} \lor \neg \left(y \leq 8 \cdot 10^{+126}\right) \land y \leq 2.6 \cdot 10^{+210}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 8: 73.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+49} \lor \neg \left(y \leq 205000\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.9e+49) (not (<= y 205000.0)))
   (* 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 <= -3.9e+49) || !(y <= 205000.0)) {
		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 <= (-3.9d+49)) .or. (.not. (y <= 205000.0d0))) 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 <= -3.9e+49) || !(y <= 205000.0)) {
		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 <= -3.9e+49) or not (y <= 205000.0):
		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 <= -3.9e+49) || !(y <= 205000.0))
		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 <= -3.9e+49) || ~((y <= 205000.0)))
		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, -3.9e+49], N[Not[LessEqual[y, 205000.0]], $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 < -3.9000000000000001e49 or 205000 < y

   1. Initial program 97.4%

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

   2. Taylor expanded in y around inf 89.1%

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

   3. Taylor expanded in t around 0 65.5%

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

   if -3.9000000000000001e49 < y < 205000

   1. Initial program 96.0%

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

   2. Taylor expanded in b around inf 81.2%

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

      1. associate-*r* 81.2%

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

      2. *-commutative 81.2%

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

      3. neg-mul-1 81.2%

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

   4. Simplified 81.2%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+49} \lor \neg \left(y \leq 205000\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 9: 54.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6e+49) (* x (- 1.0 (* y t))) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6e+49) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-6d+49)) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6e+49) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6e+49:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6e+49)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6e+49)
		tmp = x * (1.0 - (y * t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6e+49], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.0000000000000005e49

   1. Initial program 98.3%

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

   2. Taylor expanded in t around inf 84.0%

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

      1. mul-1-neg 84.0%

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

      2. distribute-rgt-neg-out 84.0%

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

   4. Simplified 84.0%

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

   5. Taylor expanded in y around 0 27.3%

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

      1. +-commutative 27.3%

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

      2. mul-1-neg 27.3%

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

      3. unsub-neg 27.3%

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

   7. Simplified 27.3%

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

   8. Taylor expanded in x around 0 35.6%

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

   if -6.0000000000000005e49 < t

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf 66.7%

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

   3. Taylor expanded in t around 0 61.8%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 10: 25.7% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(x \cdot b\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+174}:\\ \;\;\;\;t \cdot \left(-x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a) (* x b))))
   (if (<= a -1.7e+37)
     t_1
     (if (<= a 5.5e-76) x (if (<= a 1.08e+174) (* t (- (* x y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * (x * b);
	double tmp;
	if (a <= -1.7e+37) {
		tmp = t_1;
	} else if (a <= 5.5e-76) {
		tmp = x;
	} else if (a <= 1.08e+174) {
		tmp = t * -(x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a * (x * b)
    if (a <= (-1.7d+37)) then
        tmp = t_1
    else if (a <= 5.5d-76) then
        tmp = x
    else if (a <= 1.08d+174) then
        tmp = t * -(x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * (x * b);
	double tmp;
	if (a <= -1.7e+37) {
		tmp = t_1;
	} else if (a <= 5.5e-76) {
		tmp = x;
	} else if (a <= 1.08e+174) {
		tmp = t * -(x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a * (x * b)
	tmp = 0
	if a <= -1.7e+37:
		tmp = t_1
	elif a <= 5.5e-76:
		tmp = x
	elif a <= 1.08e+174:
		tmp = t * -(x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) * Float64(x * b))
	tmp = 0.0
	if (a <= -1.7e+37)
		tmp = t_1;
	elseif (a <= 5.5e-76)
		tmp = x;
	elseif (a <= 1.08e+174)
		tmp = Float64(t * Float64(-Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a * (x * b);
	tmp = 0.0;
	if (a <= -1.7e+37)
		tmp = t_1;
	elseif (a <= 5.5e-76)
		tmp = x;
	elseif (a <= 1.08e+174)
		tmp = t * -(x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * N[(x * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+37], t$95$1, If[LessEqual[a, 5.5e-76], x, If[LessEqual[a, 1.08e+174], N[(t * (-N[(x * y), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.70000000000000003e37 or 1.08e174 < a

   1. Initial program 92.1%

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

   2. Taylor expanded in b around inf 70.3%

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

      1. associate-*r* 70.3%

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

      2. *-commutative 70.3%

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

      3. neg-mul-1 70.3%

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

   4. Simplified 70.3%

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

   5. Taylor expanded in b around 0 30.2%

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

      1. mul-1-neg 30.2%

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

      2. unsub-neg 30.2%

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

   7. Simplified 30.2%

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

   8. Taylor expanded in a around inf 27.5%

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

      1. associate-*r* 27.5%

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

      2. neg-mul-1 27.5%

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

   10. Simplified 27.5%

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

   if -1.70000000000000003e37 < a < 5.50000000000000014e-76

   1. Initial program 99.4%

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

   2. Taylor expanded in b around inf 53.3%

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

      1. associate-*r* 53.3%

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

      2. *-commutative 53.3%

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

      3. neg-mul-1 53.3%

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

   4. Simplified 53.3%

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

   5. Taylor expanded in b around 0 35.9%

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

   if 5.50000000000000014e-76 < a < 1.08e174

   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. Taylor expanded in t around inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. distribute-rgt-neg-out 53.7%

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

   4. Simplified 53.7%

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

   5. Taylor expanded in y around 0 16.2%

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

      1. +-commutative 16.2%

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

      2. mul-1-neg 16.2%

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

      3. unsub-neg 16.2%

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

   7. Simplified 16.2%

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

   8. Taylor expanded in y around inf 26.2%

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

      1. neg-mul-1 26.2%

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

      2. distribute-rgt-neg-in 26.2%

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

   10. Simplified 26.2%

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

   11. Taylor expanded in y around 0 26.2%

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

       1. mul-1-neg 26.2%

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

       2. associate-*r* 29.8%

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

       3. *-commutative 29.8%

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

       4. associate-*r* 28.4%

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

       5. distribute-rgt-neg-in 28.4%

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

       6. distribute-rgt-neg-in 28.4%

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

   13. Simplified 28.4%

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

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+37}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+174}:\\ \;\;\;\;t \cdot \left(-x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot b\right)\\ \end{array} \]

Alternative 11: 26.1% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+35}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(-x\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+174}:\\ \;\;\;\;t \cdot \left(-x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.45e+35)
   (* (* a b) (- x))
   (if (<= a 1.08e-75)
     x
     (if (<= a 1.22e+174) (* t (- (* x y))) (* (- a) (* x b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.45e+35) {
		tmp = (a * b) * -x;
	} else if (a <= 1.08e-75) {
		tmp = x;
	} else if (a <= 1.22e+174) {
		tmp = t * -(x * y);
	} else {
		tmp = -a * (x * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.45d+35)) then
        tmp = (a * b) * -x
    else if (a <= 1.08d-75) then
        tmp = x
    else if (a <= 1.22d+174) then
        tmp = t * -(x * y)
    else
        tmp = -a * (x * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.45e+35) {
		tmp = (a * b) * -x;
	} else if (a <= 1.08e-75) {
		tmp = x;
	} else if (a <= 1.22e+174) {
		tmp = t * -(x * y);
	} else {
		tmp = -a * (x * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.45e+35:
		tmp = (a * b) * -x
	elif a <= 1.08e-75:
		tmp = x
	elif a <= 1.22e+174:
		tmp = t * -(x * y)
	else:
		tmp = -a * (x * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.45e+35)
		tmp = Float64(Float64(a * b) * Float64(-x));
	elseif (a <= 1.08e-75)
		tmp = x;
	elseif (a <= 1.22e+174)
		tmp = Float64(t * Float64(-Float64(x * y)));
	else
		tmp = Float64(Float64(-a) * Float64(x * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.45e+35)
		tmp = (a * b) * -x;
	elseif (a <= 1.08e-75)
		tmp = x;
	elseif (a <= 1.22e+174)
		tmp = t * -(x * y);
	else
		tmp = -a * (x * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.45e+35], N[(N[(a * b), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[a, 1.08e-75], x, If[LessEqual[a, 1.22e+174], N[(t * (-N[(x * y), $MachinePrecision])), $MachinePrecision], N[((-a) * N[(x * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.45000000000000013e35

   1. Initial program 90.4%

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

   2. Taylor expanded in b around inf 62.4%

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

      1. associate-*r* 62.4%

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

      2. *-commutative 62.4%

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

      3. neg-mul-1 62.4%

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

   4. Simplified 62.4%

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

   5. Taylor expanded in b around 0 24.2%

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

      1. mul-1-neg 24.2%

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

      2. unsub-neg 24.2%

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

   7. Simplified 24.2%

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

   8. Taylor expanded in a around inf 19.2%

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

      1. associate-*r* 19.2%

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

      2. neg-mul-1 19.2%

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

   10. Simplified 19.2%

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

   11. Taylor expanded in a around 0 19.2%

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

       1. mul-1-neg 19.2%

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

       2. associate-*r* 28.4%

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

       3. distribute-rgt-neg-in 28.4%

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

   13. Simplified 28.4%

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

   if -2.45000000000000013e35 < a < 1.08e-75

   1. Initial program 99.4%

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

   2. Taylor expanded in b around inf 53.3%

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

      1. associate-*r* 53.3%

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

      2. *-commutative 53.3%

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

      3. neg-mul-1 53.3%

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

   4. Simplified 53.3%

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

   5. Taylor expanded in b around 0 35.9%

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

   if 1.08e-75 < a < 1.21999999999999996e174

   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. Taylor expanded in t around inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. distribute-rgt-neg-out 53.7%

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

   4. Simplified 53.7%

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

   5. Taylor expanded in y around 0 16.2%

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

      1. +-commutative 16.2%

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

      2. mul-1-neg 16.2%

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

      3. unsub-neg 16.2%

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

   7. Simplified 16.2%

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

   8. Taylor expanded in y around inf 26.2%

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

      1. neg-mul-1 26.2%

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

      2. distribute-rgt-neg-in 26.2%

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

   10. Simplified 26.2%

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

   11. Taylor expanded in y around 0 26.2%

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

       1. mul-1-neg 26.2%

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

       2. associate-*r* 29.8%

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

       3. *-commutative 29.8%

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

       4. associate-*r* 28.4%

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

       5. distribute-rgt-neg-in 28.4%

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

       6. distribute-rgt-neg-in 28.4%

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

   13. Simplified 28.4%

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

   if 1.21999999999999996e174 < a

   1. Initial program 94.2%

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

   2. Taylor expanded in b around inf 79.9%

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

      1. associate-*r* 79.9%

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

      2. *-commutative 79.9%

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

      3. neg-mul-1 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in b around 0 37.5%

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

      1. mul-1-neg 37.5%

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

      2. unsub-neg 37.5%

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

   7. Simplified 37.5%

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

   8. Taylor expanded in a around inf 37.5%

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

      1. associate-*r* 37.5%

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

      2. neg-mul-1 37.5%

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

   10. Simplified 37.5%

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

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+35}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(-x\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+174}:\\ \;\;\;\;t \cdot \left(-x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot b\right)\\ \end{array} \]

Alternative 12: 34.1% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \left(-x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2e+56)
   (* t (- (* x y)))
   (if (<= y 2.9e-6) (* x (- 1.0 (* a b))) (* (* a b) (- x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2e+56) {
		tmp = t * -(x * y);
	} else if (y <= 2.9e-6) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = (a * b) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2d+56)) then
        tmp = t * -(x * y)
    else if (y <= 2.9d-6) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = (a * b) * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2e+56) {
		tmp = t * -(x * y);
	} else if (y <= 2.9e-6) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = (a * b) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2e+56:
		tmp = t * -(x * y)
	elif y <= 2.9e-6:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = (a * b) * -x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2e+56)
		tmp = Float64(t * Float64(-Float64(x * y)));
	elseif (y <= 2.9e-6)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(Float64(a * b) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2e+56)
		tmp = t * -(x * y);
	elseif (y <= 2.9e-6)
		tmp = x * (1.0 - (a * b));
	else
		tmp = (a * b) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2e+56], N[(t * (-N[(x * y), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 2.9e-6], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.00000000000000018e56

   1. Initial program 98.2%

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

   2. Taylor expanded in t around inf 61.3%

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

      1. mul-1-neg 61.3%

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

      2. distribute-rgt-neg-out 61.3%

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

   4. Simplified 61.3%

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

   5. Taylor expanded in y around 0 13.7%

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

      1. +-commutative 13.7%

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

      2. mul-1-neg 13.7%

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

      3. unsub-neg 13.7%

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

   7. Simplified 13.7%

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

   8. Taylor expanded in y around inf 16.9%

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

      1. neg-mul-1 16.9%

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

      2. distribute-rgt-neg-in 16.9%

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

   10. Simplified 16.9%

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

   11. Taylor expanded in y around 0 16.9%

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

       1. mul-1-neg 16.9%

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

       2. associate-*r* 18.5%

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

       3. *-commutative 18.5%

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

       4. associate-*r* 22.1%

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

       5. distribute-rgt-neg-in 22.1%

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

       6. distribute-rgt-neg-in 22.1%

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

   13. Simplified 22.1%

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

   if -2.00000000000000018e56 < y < 2.9000000000000002e-6

   1. Initial program 96.0%

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

   2. Taylor expanded in b around inf 80.7%

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

      1. associate-*r* 80.7%

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

      2. *-commutative 80.7%

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

      3. neg-mul-1 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in b around 0 44.9%

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

      1. mul-1-neg 44.9%

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

      2. unsub-neg 44.9%

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

   7. Simplified 44.9%

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

   if 2.9000000000000002e-6 < y

   1. Initial program 96.7%

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

   2. Taylor expanded in b around inf 36.4%

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

      1. associate-*r* 36.4%

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

      2. *-commutative 36.4%

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

      3. neg-mul-1 36.4%

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

   4. Simplified 36.4%

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

   5. Taylor expanded in b around 0 15.7%

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

      1. mul-1-neg 15.7%

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

      2. unsub-neg 15.7%

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

   7. Simplified 15.7%

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

   8. Taylor expanded in a around inf 23.8%

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

      1. associate-*r* 23.8%

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

      2. neg-mul-1 23.8%

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

   10. Simplified 23.8%

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

   11. Taylor expanded in a around 0 23.8%

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

       1. mul-1-neg 23.8%

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

       2. associate-*r* 31.5%

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

       3. distribute-rgt-neg-in 31.5%

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

   13. Simplified 31.5%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \left(-x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(-x\right)\\ \end{array} \]

Alternative 13: 27.0% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -640000000000 \lor \neg \left(y \leq 1.3 \cdot 10^{+14}\right):\\ \;\;\;\;t \cdot \left(-x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -640000000000.0) (not (<= y 1.3e+14))) (* t (- (* x y))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -640000000000.0) || !(y <= 1.3e+14)) {
		tmp = t * -(x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-640000000000.0d0)) .or. (.not. (y <= 1.3d+14))) then
        tmp = t * -(x * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -640000000000.0) || !(y <= 1.3e+14)) {
		tmp = t * -(x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -640000000000.0) or not (y <= 1.3e+14):
		tmp = t * -(x * y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -640000000000.0) || !(y <= 1.3e+14))
		tmp = Float64(t * Float64(-Float64(x * y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -640000000000.0) || ~((y <= 1.3e+14)))
		tmp = t * -(x * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -640000000000.0], N[Not[LessEqual[y, 1.3e+14]], $MachinePrecision]], N[(t * (-N[(x * y), $MachinePrecision])), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.4e11 or 1.3e14 < y

   1. Initial program 97.5%

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

   2. Taylor expanded in t around inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. distribute-rgt-neg-out 56.0%

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

   4. Simplified 56.0%

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

   5. Taylor expanded in y around 0 13.7%

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

      1. +-commutative 13.7%

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

      2. mul-1-neg 13.7%

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

      3. unsub-neg 13.7%

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

   7. Simplified 13.7%

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

   8. Taylor expanded in y around inf 20.5%

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

      1. neg-mul-1 20.5%

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

      2. distribute-rgt-neg-in 20.5%

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

   10. Simplified 20.5%

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

   11. Taylor expanded in y around 0 20.5%

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

       1. mul-1-neg 20.5%

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

       2. associate-*r* 23.8%

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

       3. *-commutative 23.8%

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

       4. associate-*r* 21.5%

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

       5. distribute-rgt-neg-in 21.5%

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

       6. distribute-rgt-neg-in 21.5%

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

   13. Simplified 21.5%

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

   if -6.4e11 < y < 1.3e14

   1. Initial program 95.9%

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

   2. Taylor expanded in b around inf 79.9%

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

      1. associate-*r* 79.9%

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

      2. *-commutative 79.9%

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

      3. neg-mul-1 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in b around 0 35.5%

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

4. Final simplification 28.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -640000000000 \lor \neg \left(y \leq 1.3 \cdot 10^{+14}\right):\\ \;\;\;\;t \cdot \left(-x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 28.5% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -560000000000:\\ \;\;\;\;t \cdot \left(-x \cdot y\right)\\ \mathbf{elif}\;y \leq 135000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -560000000000.0)
   (* t (- (* x y)))
   (if (<= y 135000000.0) x (* (* x t) (- y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -560000000000.0) {
		tmp = t * -(x * y);
	} else if (y <= 135000000.0) {
		tmp = x;
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-560000000000.0d0)) then
        tmp = t * -(x * y)
    else if (y <= 135000000.0d0) then
        tmp = x
    else
        tmp = (x * t) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -560000000000.0) {
		tmp = t * -(x * y);
	} else if (y <= 135000000.0) {
		tmp = x;
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -560000000000.0:
		tmp = t * -(x * y)
	elif y <= 135000000.0:
		tmp = x
	else:
		tmp = (x * t) * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -560000000000.0)
		tmp = Float64(t * Float64(-Float64(x * y)));
	elseif (y <= 135000000.0)
		tmp = x;
	else
		tmp = Float64(Float64(x * t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -560000000000.0)
		tmp = t * -(x * y);
	elseif (y <= 135000000.0)
		tmp = x;
	else
		tmp = (x * t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -560000000000.0], N[(t * (-N[(x * y), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 135000000.0], x, N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.6e11

   1. Initial program 98.5%

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

   2. Taylor expanded in t around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. distribute-rgt-neg-out 57.5%

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

   4. Simplified 57.5%

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

   5. Taylor expanded in y around 0 12.0%

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

      1. +-commutative 12.0%

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

      2. mul-1-neg 12.0%

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

      3. unsub-neg 12.0%

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

   7. Simplified 12.0%

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

   8. Taylor expanded in y around inf 15.9%

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

      1. neg-mul-1 15.9%

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

      2. distribute-rgt-neg-in 15.9%

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

   10. Simplified 15.9%

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

   11. Taylor expanded in y around 0 15.9%

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

       1. mul-1-neg 15.9%

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

       2. associate-*r* 17.3%

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

       3. *-commutative 17.3%

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

       4. associate-*r* 20.2%

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

       5. distribute-rgt-neg-in 20.2%

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

       6. distribute-rgt-neg-in 20.2%

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

   13. Simplified 20.2%

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

   if -5.6e11 < y < 1.35e8

   1. Initial program 95.8%

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

   2. Taylor expanded in b around inf 81.0%

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

      1. associate-*r* 81.0%

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

      2. *-commutative 81.0%

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

      3. neg-mul-1 81.0%

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

   4. Simplified 81.0%

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

   5. Taylor expanded in b around 0 36.0%

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

   if 1.35e8 < y

   1. Initial program 96.5%

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

   2. Taylor expanded in t around inf 54.0%

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

      1. mul-1-neg 54.0%

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

      2. distribute-rgt-neg-out 54.0%

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

   4. Simplified 54.0%

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

   5. Taylor expanded in y around 0 15.3%

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

      1. +-commutative 15.3%

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

      2. mul-1-neg 15.3%

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

      3. unsub-neg 15.3%

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

   7. Simplified 15.3%

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

   8. Taylor expanded in y around inf 25.2%

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

      1. neg-mul-1 25.2%

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

      2. distribute-rgt-neg-in 25.2%

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

   10. Simplified 25.2%

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

4. Final simplification 29.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -560000000000:\\ \;\;\;\;t \cdot \left(-x \cdot y\right)\\ \mathbf{elif}\;y \leq 135000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \]

Alternative 15: 24.1% accurate, 34.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+14} \lor \neg \left(y \leq 4 \cdot 10^{+42}\right):\\ \;\;\;\;b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.7e+14) (not (<= y 4e+42))) (* b (* x a)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.7e+14) || !(y <= 4e+42)) {
		tmp = b * (x * a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.7d+14)) .or. (.not. (y <= 4d+42))) then
        tmp = b * (x * a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.7e+14) || !(y <= 4e+42)) {
		tmp = b * (x * a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.7e+14) or not (y <= 4e+42):
		tmp = b * (x * a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.7e+14) || !(y <= 4e+42))
		tmp = Float64(b * Float64(x * a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.7e+14) || ~((y <= 4e+42)))
		tmp = b * (x * a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.7e+14], N[Not[LessEqual[y, 4e+42]], $MachinePrecision]], N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.7e14 or 4.00000000000000018e42 < y

   1. Initial program 97.4%

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

   2. Taylor expanded in b around inf 35.4%

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

      1. associate-*r* 35.4%

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

      2. *-commutative 35.4%

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

      3. neg-mul-1 35.4%

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

   4. Simplified 35.4%

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

   5. Taylor expanded in b around 0 11.7%

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

      1. mul-1-neg 11.7%

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

      2. unsub-neg 11.7%

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

   7. Simplified 11.7%

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

   8. Taylor expanded in a around inf 18.1%

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

      1. associate-*r* 18.1%

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

      2. neg-mul-1 18.1%

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

   10. Simplified 18.1%

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

       1. expm1-log1p-u 14.0%

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

       2. expm1-udef 28.7%

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

       3. add-sqr-sqrt 9.9%

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

       4. sqrt-unprod 27.6%

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

       5. sqr-neg 27.6%

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

       6. sqrt-unprod 16.1%

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

       7. add-sqr-sqrt 25.3%

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

       8. associate-*r* 25.3%

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

   12. Applied egg-rr 25.3%

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

       1. expm1-def 14.7%

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

       2. expm1-log1p 16.0%

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

       3. associate-*r* 12.7%

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

       4. *-commutative 12.7%

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

       5. associate-*l* 16.8%

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

   14. Simplified 16.8%

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

   if -4.7e14 < y < 4.00000000000000018e42

   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. Taylor expanded in b around inf 79.3%

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

      1. associate-*r* 79.3%

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

      2. *-commutative 79.3%

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

      3. neg-mul-1 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in b around 0 34.2%

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

4. Final simplification 26.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+14} \lor \neg \left(y \leq 4 \cdot 10^{+42}\right):\\ \;\;\;\;b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 22.3% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.1 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 5.1e+42) x (* a (* x b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 5.1e+42) {
		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 <= 5.1d+42) 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 <= 5.1e+42) {
		tmp = x;
	} else {
		tmp = a * (x * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 5.1e+42:
		tmp = x
	else:
		tmp = a * (x * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 5.1e+42)
		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 <= 5.1e+42)
		tmp = x;
	else
		tmp = a * (x * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 5.1e+42], x, N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.0999999999999999e42

   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. Taylor expanded in b around inf 65.3%

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

      1. associate-*r* 65.3%

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

      2. *-commutative 65.3%

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

      3. neg-mul-1 65.3%

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

   4. Simplified 65.3%

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

   5. Taylor expanded in b around 0 24.8%

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

   if 5.0999999999999999e42 < y

   1. Initial program 96.0%

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

   2. Taylor expanded in b around inf 36.1%

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

      1. associate-*r* 36.1%

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

      2. *-commutative 36.1%

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

      3. neg-mul-1 36.1%

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

   4. Simplified 36.1%

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

   5. Taylor expanded in b around 0 12.7%

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

      1. mul-1-neg 12.7%

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

      2. unsub-neg 12.7%

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

   7. Simplified 12.7%

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

   8. Taylor expanded in a around inf 22.5%

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

      1. associate-*r* 22.5%

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

      2. neg-mul-1 22.5%

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

   10. Simplified 22.5%

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

       1. expm1-log1p-u 19.9%

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

       2. expm1-udef 36.8%

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

       3. add-sqr-sqrt 12.3%

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

       4. sqrt-unprod 34.4%

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

       5. sqr-neg 34.4%

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

       6. sqrt-unprod 20.4%

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

       7. add-sqr-sqrt 32.7%

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

       8. associate-*r* 32.8%

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

   12. Applied egg-rr 32.8%

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

       1. expm1-def 21.4%

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

       2. expm1-log1p 23.8%

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

       3. associate-*r* 18.1%

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

   14. Simplified 18.1%

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

4. Final simplification 23.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.1 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \]

Alternative 17: 20.4% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= a 2.1e-26) x (* y (* x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.1e-26) {
		tmp = x;
	} else {
		tmp = y * (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 2.1d-26) then
        tmp = x
    else
        tmp = y * (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.1e-26) {
		tmp = x;
	} else {
		tmp = y * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 2.1e-26:
		tmp = x
	else:
		tmp = y * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 2.1e-26)
		tmp = x;
	else
		tmp = Float64(y * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 2.1e-26)
		tmp = x;
	else
		tmp = y * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 2.1e-26], x, N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.10000000000000008e-26

   1. Initial program 97.4%

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

   2. Taylor expanded in b around inf 55.1%

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

      1. associate-*r* 55.1%

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

      2. *-commutative 55.1%

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

      3. neg-mul-1 55.1%

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

   4. Simplified 55.1%

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

   5. Taylor expanded in b around 0 27.0%

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

   if 2.10000000000000008e-26 < a

   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. Taylor expanded in t around inf 39.1%

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

      1. mul-1-neg 39.1%

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

      2. distribute-rgt-neg-out 39.1%

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

   4. Simplified 39.1%

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

      1. expm1-log1p-u 28.5%

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

      2. expm1-udef 41.8%

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

      3. *-commutative 41.8%

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

      4. exp-prod 40.4%

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

      5. add-sqr-sqrt 24.7%

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

      6. sqrt-unprod 45.6%

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

      7. sqr-neg 45.6%

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

      8. sqrt-unprod 20.9%

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

      9. add-sqr-sqrt 32.9%

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

   6. Applied egg-rr 32.9%

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

      1. expm1-def 19.6%

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

      2. expm1-log1p 23.8%

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

      3. exp-prod 21.4%

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

   8. Simplified 21.4%

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

   9. Taylor expanded in t around 0 9.0%

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

   10. Taylor expanded in y around inf 19.9%

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

       1. *-commutative 19.9%

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

   12. Simplified 19.9%

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

4. Final simplification 24.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 18: 19.2% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

2. Taylor expanded in b around inf 59.6%

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

   1. associate-*r* 59.6%

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

   2. *-commutative 59.6%

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

   3. neg-mul-1 59.6%

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

4. Simplified 59.6%

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

5. Taylor expanded in b around 0 20.7%

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

6. Final simplification 20.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023240 
(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))))))