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

Percentage Accurate: 96.5% → 99.6%

Time: 18.8s

Alternatives: 15

Speedup: 0.8×

• 40.9% 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: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

   1. fma-define 96.8%

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

   2. sub-neg 96.8%

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

   3. log1p-define 99.6%

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

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. Add Preprocessing

5. Final simplification 99.6%

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

Alternative 2: 88.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+223}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \mathbf{elif}\;t \leq -640:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+87}:\\ \;\;\;\;x \cdot e^{y \cdot \log z - a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* t (- y))))))
   (if (<= t -8.8e+248)
     t_1
     (if (<= t -7.5e+223)
       (* x (exp (* a (- (+ z b)))))
       (if (<= t -640.0)
         t_1
         (if (<= t 3.8e+87)
           (* x (exp (- (* y (log z)) (* a b))))
           (* x (exp (* y (- (log z) t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((t * -y));
	double tmp;
	if (t <= -8.8e+248) {
		tmp = t_1;
	} else if (t <= -7.5e+223) {
		tmp = x * exp((a * -(z + b)));
	} else if (t <= -640.0) {
		tmp = t_1;
	} else if (t <= 3.8e+87) {
		tmp = x * exp(((y * log(z)) - (a * b)));
	} else {
		tmp = x * exp((y * (log(z) - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * exp((t * -y))
    if (t <= (-8.8d+248)) then
        tmp = t_1
    else if (t <= (-7.5d+223)) then
        tmp = x * exp((a * -(z + b)))
    else if (t <= (-640.0d0)) then
        tmp = t_1
    else if (t <= 3.8d+87) then
        tmp = x * exp(((y * log(z)) - (a * b)))
    else
        tmp = x * exp((y * (log(z) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((t * -y));
	double tmp;
	if (t <= -8.8e+248) {
		tmp = t_1;
	} else if (t <= -7.5e+223) {
		tmp = x * Math.exp((a * -(z + b)));
	} else if (t <= -640.0) {
		tmp = t_1;
	} else if (t <= 3.8e+87) {
		tmp = x * Math.exp(((y * Math.log(z)) - (a * b)));
	} else {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((t * -y))
	tmp = 0
	if t <= -8.8e+248:
		tmp = t_1
	elif t <= -7.5e+223:
		tmp = x * math.exp((a * -(z + b)))
	elif t <= -640.0:
		tmp = t_1
	elif t <= 3.8e+87:
		tmp = x * math.exp(((y * math.log(z)) - (a * b)))
	else:
		tmp = x * math.exp((y * (math.log(z) - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(t * Float64(-y))))
	tmp = 0.0
	if (t <= -8.8e+248)
		tmp = t_1;
	elseif (t <= -7.5e+223)
		tmp = Float64(x * exp(Float64(a * Float64(-Float64(z + b)))));
	elseif (t <= -640.0)
		tmp = t_1;
	elseif (t <= 3.8e+87)
		tmp = Float64(x * exp(Float64(Float64(y * log(z)) - Float64(a * b))));
	else
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((t * -y));
	tmp = 0.0;
	if (t <= -8.8e+248)
		tmp = t_1;
	elseif (t <= -7.5e+223)
		tmp = x * exp((a * -(z + b)));
	elseif (t <= -640.0)
		tmp = t_1;
	elseif (t <= 3.8e+87)
		tmp = x * exp(((y * log(z)) - (a * b)));
	else
		tmp = x * exp((y * (log(z) - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e+248], t$95$1, If[LessEqual[t, -7.5e+223], N[(x * N[Exp[N[(a * (-N[(z + b), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -640.0], t$95$1, If[LessEqual[t, 3.8e+87], N[(x * N[Exp[N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.7999999999999997e248 or -7.5000000000000003e223 < t < -640

   1. Initial program 96.3%

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

   3. Taylor expanded in t around inf 89.1%

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

      1. mul-1-neg 89.1%

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

      2. distribute-lft-neg-out 89.1%

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

      3. *-commutative 89.1%

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

   5. Simplified 89.1%

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

   if -8.7999999999999997e248 < t < -7.5000000000000003e223

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.2%

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

      1. sub-neg 78.2%

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

      2. mul-1-neg 78.2%

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

      3. log1p-define 90.1%

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

      4. mul-1-neg 90.1%

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

   5. Simplified 90.1%

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

   6. Taylor expanded in z around 0 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

      3. mul-1-neg 90.1%

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

   8. Simplified 90.1%

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

   if -640 < t < 3.80000000000000011e87

   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. Add Preprocessing

   3. Taylor expanded in z around 0 96.2%

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

   4. Taylor expanded in t around 0 96.1%

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

      1. +-commutative 96.1%

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

      2. mul-1-neg 96.1%

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

      3. unsub-neg 96.1%

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

   6. Simplified 96.1%

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

   if 3.80000000000000011e87 < t

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 92.9%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+248}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+223}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \mathbf{elif}\;t \leq -640:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+87}:\\ \;\;\;\;x \cdot e^{y \cdot \log z - a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.25 \cdot 10^{+162} \lor \neg \left(a \leq 1.35 \cdot 10^{+55}\right) \land \left(a \leq 3.25 \cdot 10^{+97} \lor \neg \left(a \leq 3.6 \cdot 10^{+138}\right)\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.25e+162)
         (and (not (<= a 1.35e+55))
              (or (<= a 3.25e+97) (not (<= a 3.6e+138)))))
   (* x (exp (* a (- (+ z b)))))
   (* x (exp (* y (- (log z) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.25e+162) || (!(a <= 1.35e+55) && ((a <= 3.25e+97) || !(a <= 3.6e+138)))) {
		tmp = x * exp((a * -(z + b)));
	} else {
		tmp = x * exp((y * (log(z) - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-3.25d+162)) .or. (.not. (a <= 1.35d+55)) .and. (a <= 3.25d+97) .or. (.not. (a <= 3.6d+138))) then
        tmp = x * exp((a * -(z + b)))
    else
        tmp = x * exp((y * (log(z) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.25e+162) || (!(a <= 1.35e+55) && ((a <= 3.25e+97) || !(a <= 3.6e+138)))) {
		tmp = x * Math.exp((a * -(z + b)));
	} else {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.25e+162) or (not (a <= 1.35e+55) and ((a <= 3.25e+97) or not (a <= 3.6e+138))):
		tmp = x * math.exp((a * -(z + b)))
	else:
		tmp = x * math.exp((y * (math.log(z) - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.25e+162) || (!(a <= 1.35e+55) && ((a <= 3.25e+97) || !(a <= 3.6e+138))))
		tmp = Float64(x * exp(Float64(a * Float64(-Float64(z + b)))));
	else
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3.25e+162) || (~((a <= 1.35e+55)) && ((a <= 3.25e+97) || ~((a <= 3.6e+138)))))
		tmp = x * exp((a * -(z + b)));
	else
		tmp = x * exp((y * (log(z) - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.25e+162], And[N[Not[LessEqual[a, 1.35e+55]], $MachinePrecision], Or[LessEqual[a, 3.25e+97], N[Not[LessEqual[a, 3.6e+138]], $MachinePrecision]]]], N[(x * N[Exp[N[(a * (-N[(z + b), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.2500000000000002e162 or 1.34999999999999988e55 < a < 3.25e97 or 3.6000000000000001e138 < a

   1. Initial program 86.8%

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

   3. Taylor expanded in y around 0 76.7%

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

      1. sub-neg 76.7%

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

      2. mul-1-neg 76.7%

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

      3. log1p-define 89.8%

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

      4. mul-1-neg 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in z around 0 89.8%

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

      1. mul-1-neg 89.8%

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

      2. unsub-neg 89.8%

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

      3. mul-1-neg 89.8%

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

   8. Simplified 89.8%

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

   if -3.2500000000000002e162 < a < 1.34999999999999988e55 or 3.25e97 < a < 3.6000000000000001e138

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 90.9%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.25 \cdot 10^{+162} \lor \neg \left(a \leq 1.35 \cdot 10^{+55}\right) \land \left(a \leq 3.25 \cdot 10^{+97} \lor \neg \left(a \leq 3.6 \cdot 10^{+138}\right)\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.0% 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 96.0%

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

3. Taylor expanded in z around 0 96.0%

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

4. Final simplification 96.0%

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

Alternative 5: 74.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+42} \lor \neg \left(a \leq 5.2 \cdot 10^{+28}\right) \land \left(a \leq 1.45 \cdot 10^{+100} \lor \neg \left(a \leq 1.5 \cdot 10^{+139}\right)\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.8e+42)
         (and (not (<= a 5.2e+28))
              (or (<= a 1.45e+100) (not (<= a 1.5e+139)))))
   (* x (exp (* a (- (+ z b)))))
   (* x (exp (* t (- y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.8e+42) || (!(a <= 5.2e+28) && ((a <= 1.45e+100) || !(a <= 1.5e+139)))) {
		tmp = x * exp((a * -(z + b)));
	} else {
		tmp = x * exp((t * -y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-3.8d+42)) .or. (.not. (a <= 5.2d+28)) .and. (a <= 1.45d+100) .or. (.not. (a <= 1.5d+139))) then
        tmp = x * exp((a * -(z + b)))
    else
        tmp = x * exp((t * -y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.8e+42) || (!(a <= 5.2e+28) && ((a <= 1.45e+100) || !(a <= 1.5e+139)))) {
		tmp = x * Math.exp((a * -(z + b)));
	} else {
		tmp = x * Math.exp((t * -y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.8e+42) or (not (a <= 5.2e+28) and ((a <= 1.45e+100) or not (a <= 1.5e+139))):
		tmp = x * math.exp((a * -(z + b)))
	else:
		tmp = x * math.exp((t * -y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.8e+42) || (!(a <= 5.2e+28) && ((a <= 1.45e+100) || !(a <= 1.5e+139))))
		tmp = Float64(x * exp(Float64(a * Float64(-Float64(z + b)))));
	else
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3.8e+42) || (~((a <= 5.2e+28)) && ((a <= 1.45e+100) || ~((a <= 1.5e+139)))))
		tmp = x * exp((a * -(z + b)));
	else
		tmp = x * exp((t * -y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.8e+42], And[N[Not[LessEqual[a, 5.2e+28]], $MachinePrecision], Or[LessEqual[a, 1.45e+100], N[Not[LessEqual[a, 1.5e+139]], $MachinePrecision]]]], N[(x * N[Exp[N[(a * (-N[(z + b), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.7999999999999998e42 or 5.2000000000000004e28 < a < 1.45e100 or 1.5e139 < a

   1. Initial program 90.6%

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

   3. Taylor expanded in y around 0 71.2%

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

      1. sub-neg 71.2%

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

      2. mul-1-neg 71.2%

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

      3. log1p-define 82.5%

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

      4. mul-1-neg 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in z around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. unsub-neg 82.5%

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

      3. mul-1-neg 82.5%

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

   8. Simplified 82.5%

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

   if -3.7999999999999998e42 < a < 5.2000000000000004e28 or 1.45e100 < a < 1.5e139

   1. Initial program 99.3%

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

   3. Taylor expanded in t around inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. distribute-lft-neg-out 80.5%

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

      3. *-commutative 80.5%

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

   5. Simplified 80.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+42} \lor \neg \left(a \leq 5.2 \cdot 10^{+28}\right) \land \left(a \leq 1.45 \cdot 10^{+100} \lor \neg \left(a \leq 1.5 \cdot 10^{+139}\right)\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ t_2 := x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{if}\;t \leq -500:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-262}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))) (t_2 (* x (exp (* t (- y))))))
   (if (<= t -500.0)
     t_2
     (if (<= t -1.5e-260)
       t_1
       (if (<= t 7e-262)
         (* x (exp (* a (- b))))
         (if (<= t 1.2e+41) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double t_2 = x * exp((t * -y));
	double tmp;
	if (t <= -500.0) {
		tmp = t_2;
	} else if (t <= -1.5e-260) {
		tmp = t_1;
	} else if (t <= 7e-262) {
		tmp = x * exp((a * -b));
	} else if (t <= 1.2e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z ** y)
    t_2 = x * exp((t * -y))
    if (t <= (-500.0d0)) then
        tmp = t_2
    else if (t <= (-1.5d-260)) then
        tmp = t_1
    else if (t <= 7d-262) then
        tmp = x * exp((a * -b))
    else if (t <= 1.2d+41) 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.pow(z, y);
	double t_2 = x * Math.exp((t * -y));
	double tmp;
	if (t <= -500.0) {
		tmp = t_2;
	} else if (t <= -1.5e-260) {
		tmp = t_1;
	} else if (t <= 7e-262) {
		tmp = x * Math.exp((a * -b));
	} else if (t <= 1.2e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	t_2 = x * math.exp((t * -y))
	tmp = 0
	if t <= -500.0:
		tmp = t_2
	elif t <= -1.5e-260:
		tmp = t_1
	elif t <= 7e-262:
		tmp = x * math.exp((a * -b))
	elif t <= 1.2e+41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	t_2 = Float64(x * exp(Float64(t * Float64(-y))))
	tmp = 0.0
	if (t <= -500.0)
		tmp = t_2;
	elseif (t <= -1.5e-260)
		tmp = t_1;
	elseif (t <= 7e-262)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif (t <= 1.2e+41)
		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 * (z ^ y);
	t_2 = x * exp((t * -y));
	tmp = 0.0;
	if (t <= -500.0)
		tmp = t_2;
	elseif (t <= -1.5e-260)
		tmp = t_1;
	elseif (t <= 7e-262)
		tmp = x * exp((a * -b));
	elseif (t <= 1.2e+41)
		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[Power[z, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -500.0], t$95$2, If[LessEqual[t, -1.5e-260], t$95$1, If[LessEqual[t, 7e-262], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+41], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -500 or 1.2000000000000001e41 < 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. Add Preprocessing

   3. Taylor expanded in t around inf 85.2%

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

      1. mul-1-neg 85.2%

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

      2. distribute-lft-neg-out 85.2%

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

      3. *-commutative 85.2%

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

   5. Simplified 85.2%

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

   if -500 < t < -1.5e-260 or 7.00000000000000023e-262 < t < 1.2000000000000001e41

   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. Add Preprocessing

   3. Taylor expanded in y around inf 73.2%

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

   4. Taylor expanded in t around 0 73.2%

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

   if -1.5e-260 < t < 7.00000000000000023e-262

   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. Add Preprocessing

   3. Taylor expanded in b around inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-rgt-neg-out 82.5%

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

   5. Simplified 82.5%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -500:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-260}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-262}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+41}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+38} \lor \neg \left(y \leq 0.0013\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.3e+38) (not (<= y 0.0013)))
   (* x (pow z y))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e+38) || !(y <= 0.0013)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp((a * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.3d+38)) .or. (.not. (y <= 0.0013d0))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp((a * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e+38) || !(y <= 0.0013)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.3e+38) or not (y <= 0.0013):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.3e+38) || !(y <= 0.0013))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.3e+38) || ~((y <= 0.0013)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.3e+38], N[Not[LessEqual[y, 0.0013]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e38 or 0.0012999999999999999 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 92.1%

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

   4. Taylor expanded in t around 0 70.5%

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

   if -1.3e38 < y < 0.0012999999999999999

   1. Initial program 94.3%

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

   3. Taylor expanded in b around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-rgt-neg-out 70.7%

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

   5. Simplified 70.7%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+38} \lor \neg \left(y \leq 0.0013\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -420:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -420.0) (* x (- 1.0 (* y t))) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -420.0) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-420.0d0)) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -420.0) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -420.0:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -420.0)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -420.0)
		tmp = x * (1.0 - (y * t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -420.0], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -420

   1. Initial program 96.8%

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

   3. Taylor expanded in t around inf 82.6%

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

      1. mul-1-neg 82.6%

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

      2. distribute-lft-neg-out 82.6%

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

      3. *-commutative 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in y around 0 29.2%

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

      1. associate-*r* 29.2%

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

      2. mul-1-neg 29.2%

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

      3. *-commutative 29.2%

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

   8. Simplified 29.2%

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

   9. Taylor expanded in x around 0 33.8%

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

       1. mul-1-neg 33.8%

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

       2. *-commutative 33.8%

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

       3. sub-neg 33.8%

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

   11. Simplified 33.8%

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

   if -420 < t

   1. Initial program 95.7%

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

   3. Taylor expanded in y around inf 76.7%

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

   4. Taylor expanded in t around 0 67.2%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -420:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 33.0% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-5} \lor \neg \left(y \leq 1.8 \cdot 10^{-6}\right):\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.5e-5) (not (<= y 1.8e-6)))
   (* b (* x (- a)))
   (* x (- 1.0 (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e-5) || !(y <= 1.8e-6)) {
		tmp = b * (x * -a);
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9.5d-5)) .or. (.not. (y <= 1.8d-6))) then
        tmp = b * (x * -a)
    else
        tmp = x * (1.0d0 - (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e-5) || !(y <= 1.8e-6)) {
		tmp = b * (x * -a);
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9.5e-5) or not (y <= 1.8e-6):
		tmp = b * (x * -a)
	else:
		tmp = x * (1.0 - (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9.5e-5) || !(y <= 1.8e-6))
		tmp = Float64(b * Float64(x * Float64(-a)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9.5e-5) || ~((y <= 1.8e-6)))
		tmp = b * (x * -a);
	else
		tmp = x * (1.0 - (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9.5e-5], N[Not[LessEqual[y, 1.8e-6]], $MachinePrecision]], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000005e-5 or 1.79999999999999992e-6 < y

   1. Initial program 97.2%

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

   3. Taylor expanded in b around inf 31.6%

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

      1. mul-1-neg 31.6%

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

      2. distribute-rgt-neg-out 31.6%

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

   5. Simplified 31.6%

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

   6. Taylor expanded in a around 0 11.3%

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

      1. mul-1-neg 11.3%

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

      2. unsub-neg 11.3%

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

   8. Simplified 11.3%

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

   9. Taylor expanded in a around inf 20.2%

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

       1. mul-1-neg 20.2%

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

       2. *-commutative 20.2%

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

       3. associate-*r* 22.8%

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

       4. distribute-lft-neg-in 22.8%

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

       5. *-commutative 22.8%

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

   11. Simplified 22.8%

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

   if -9.5000000000000005e-5 < y < 1.79999999999999992e-6

   1. Initial program 94.3%

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

   3. Taylor expanded in b around inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. distribute-rgt-neg-out 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in a around 0 48.2%

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

      1. mul-1-neg 48.2%

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

      2. unsub-neg 48.2%

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

   8. Simplified 48.2%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-5} \lor \neg \left(y \leq 1.8 \cdot 10^{-6}\right):\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 32.8% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.5e+54)
   (* x (- 1.0 (* a b)))
   (if (<= a 5e+145) (* x (- 1.0 (* y t))) (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.5e+54) {
		tmp = x * (1.0 - (a * b));
	} else if (a <= 5e+145) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-5.5d+54)) then
        tmp = x * (1.0d0 - (a * b))
    else if (a <= 5d+145) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.5e+54) {
		tmp = x * (1.0 - (a * b));
	} else if (a <= 5e+145) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.5e+54:
		tmp = x * (1.0 - (a * b))
	elif a <= 5e+145:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.5e+54)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (a <= 5e+145)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.5e+54)
		tmp = x * (1.0 - (a * b));
	elseif (a <= 5e+145)
		tmp = x * (1.0 - (y * t));
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.5e+54], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+145], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.50000000000000026e54

   1. Initial program 91.4%

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

   3. Taylor expanded in b around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-rgt-neg-out 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in a around 0 35.0%

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

      1. mul-1-neg 35.0%

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

      2. unsub-neg 35.0%

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

   8. Simplified 35.0%

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

   if -5.50000000000000026e54 < a < 4.99999999999999967e145

   1. Initial program 98.6%

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

   3. Taylor expanded in t around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. distribute-lft-neg-out 75.7%

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

      3. *-commutative 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in y around 0 33.7%

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

      1. associate-*r* 33.7%

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

      2. mul-1-neg 33.7%

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

      3. *-commutative 33.7%

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

   8. Simplified 33.7%

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

   9. Taylor expanded in x around 0 35.3%

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

       1. mul-1-neg 35.3%

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

       2. *-commutative 35.3%

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

       3. sub-neg 35.3%

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

   11. Simplified 35.3%

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

   if 4.99999999999999967e145 < a

   1. Initial program 87.0%

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

   3. Taylor expanded in b around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-rgt-neg-out 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in a around 0 25.7%

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

      1. mul-1-neg 25.7%

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

      2. unsub-neg 25.7%

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

   8. Simplified 25.7%

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

   9. Taylor expanded in a around inf 38.3%

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

       1. mul-1-neg 38.3%

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

       2. distribute-rgt-neg-in 38.3%

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

       3. distribute-rgt-neg-in 38.3%

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

   11. Simplified 38.3%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 33.2% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.48 \cdot 10^{+57}:\\ \;\;\;\;x - \left(z + b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.48e+57)
   (- x (* (+ z b) (* x a)))
   (if (<= a 3.3e+142) (* x (- 1.0 (* y t))) (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.48e+57) {
		tmp = x - ((z + b) * (x * a));
	} else if (a <= 3.3e+142) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.48d+57)) then
        tmp = x - ((z + b) * (x * a))
    else if (a <= 3.3d+142) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.48e+57) {
		tmp = x - ((z + b) * (x * a));
	} else if (a <= 3.3e+142) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.48e+57:
		tmp = x - ((z + b) * (x * a))
	elif a <= 3.3e+142:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.48e+57)
		tmp = Float64(x - Float64(Float64(z + b) * Float64(x * a)));
	elseif (a <= 3.3e+142)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.48e+57)
		tmp = x - ((z + b) * (x * a));
	elseif (a <= 3.3e+142)
		tmp = x * (1.0 - (y * t));
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.48e+57], N[(x - N[(N[(z + b), $MachinePrecision] * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+142], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.47999999999999999e57

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0 70.8%

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

      1. sub-neg 70.8%

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

      2. mul-1-neg 70.8%

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

      3. log1p-define 77.1%

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

      4. mul-1-neg 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in z around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. unsub-neg 77.1%

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

      3. mul-1-neg 77.1%

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

   8. Simplified 77.1%

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

   9. Taylor expanded in a around 0 31.0%

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

       1. mul-1-neg 31.0%

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

       2. unsub-neg 31.0%

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

       3. associate-*r* 36.8%

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

       4. *-commutative 36.8%

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

   11. Simplified 36.8%

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

   if -1.47999999999999999e57 < a < 3.3000000000000002e142

   1. Initial program 98.6%

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

   3. Taylor expanded in t around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. distribute-lft-neg-out 75.7%

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

      3. *-commutative 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in y around 0 33.7%

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

      1. associate-*r* 33.7%

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

      2. mul-1-neg 33.7%

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

      3. *-commutative 33.7%

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

   8. Simplified 33.7%

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

   9. Taylor expanded in x around 0 35.3%

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

       1. mul-1-neg 35.3%

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

       2. *-commutative 35.3%

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

       3. sub-neg 35.3%

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

   11. Simplified 35.3%

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

   if 3.3000000000000002e142 < a

   1. Initial program 87.0%

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

   3. Taylor expanded in b around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-rgt-neg-out 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in a around 0 25.7%

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

      1. mul-1-neg 25.7%

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

      2. unsub-neg 25.7%

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

   8. Simplified 25.7%

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

   9. Taylor expanded in a around inf 38.3%

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

       1. mul-1-neg 38.3%

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

       2. distribute-rgt-neg-in 38.3%

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

       3. distribute-rgt-neg-in 38.3%

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

   11. Simplified 38.3%

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

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.48 \cdot 10^{+57}:\\ \;\;\;\;x - \left(z + b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 27.0% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-107} \lor \neg \left(y \leq 1400000\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.75e-107) (not (<= y 1400000.0))) (* a (* x (- b))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.75e-107) || !(y <= 1400000.0)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.75d-107)) .or. (.not. (y <= 1400000.0d0))) then
        tmp = a * (x * -b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.75e-107) || !(y <= 1400000.0)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.75e-107) or not (y <= 1400000.0):
		tmp = a * (x * -b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.75e-107) || !(y <= 1400000.0))
		tmp = Float64(a * Float64(x * Float64(-b)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.75e-107) || ~((y <= 1400000.0)))
		tmp = a * (x * -b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.75e-107], N[Not[LessEqual[y, 1400000.0]], $MachinePrecision]], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.74999999999999993e-107 or 1.4e6 < y

   1. Initial program 96.8%

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

   3. Taylor expanded in b around inf 33.5%

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

      1. mul-1-neg 33.5%

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

      2. distribute-rgt-neg-out 33.5%

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

   5. Simplified 33.5%

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

   6. Taylor expanded in a around 0 12.6%

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

      1. mul-1-neg 12.6%

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

      2. unsub-neg 12.6%

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

   8. Simplified 12.6%

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

   9. Taylor expanded in a around inf 19.9%

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

       1. mul-1-neg 19.9%

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

       2. distribute-rgt-neg-in 19.9%

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

       3. distribute-rgt-neg-in 19.9%

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

   11. Simplified 19.9%

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

   if -2.74999999999999993e-107 < y < 1.4e6

   1. Initial program 94.6%

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

   3. Taylor expanded in b around inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. distribute-rgt-neg-out 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in a around 0 42.0%

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

4. Final simplification 28.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-107} \lor \neg \left(y \leq 1400000\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.3% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-107} \lor \neg \left(y \leq 1.72 \cdot 10^{-6}\right):\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.75e-107) (not (<= y 1.72e-6))) (* b (* x (- a))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.75e-107) || !(y <= 1.72e-6)) {
		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 <= (-2.75d-107)) .or. (.not. (y <= 1.72d-6))) 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 <= -2.75e-107) || !(y <= 1.72e-6)) {
		tmp = b * (x * -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.75e-107) or not (y <= 1.72e-6):
		tmp = b * (x * -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.75e-107) || !(y <= 1.72e-6))
		tmp = Float64(b * Float64(x * Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.75e-107) || ~((y <= 1.72e-6)))
		tmp = b * (x * -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.75e-107], N[Not[LessEqual[y, 1.72e-6]], $MachinePrecision]], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.74999999999999993e-107 or 1.72e-6 < y

   1. Initial program 96.9%

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

   3. Taylor expanded in b around inf 34.1%

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

      1. mul-1-neg 34.1%

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

      2. distribute-rgt-neg-out 34.1%

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

   5. Simplified 34.1%

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

   6. Taylor expanded in a around 0 12.5%

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

      1. mul-1-neg 12.5%

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

      2. unsub-neg 12.5%

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

   8. Simplified 12.5%

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

   9. Taylor expanded in a around inf 19.6%

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

       1. mul-1-neg 19.6%

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

       2. *-commutative 19.6%

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

       3. associate-*r* 22.4%

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

       4. distribute-lft-neg-in 22.4%

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

       5. *-commutative 22.4%

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

   11. Simplified 22.4%

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

   if -2.74999999999999993e-107 < y < 1.72e-6

   1. Initial program 94.3%

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

   3. Taylor expanded in b around inf 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-rgt-neg-out 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in a around 0 43.5%

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

4. Final simplification 30.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-107} \lor \neg \left(y \leq 1.72 \cdot 10^{-6}\right):\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.1% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-5} \lor \neg \left(y \leq 1400000\right):\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.05e-5) (not (<= y 1400000.0))) (* a (* x b)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e-5) || !(y <= 1400000.0)) {
		tmp = a * (x * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.05d-5)) .or. (.not. (y <= 1400000.0d0))) then
        tmp = a * (x * b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e-5) || !(y <= 1400000.0)) {
		tmp = a * (x * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.05e-5) or not (y <= 1400000.0):
		tmp = a * (x * b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.05e-5) || !(y <= 1400000.0))
		tmp = Float64(a * Float64(x * b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.05e-5) || ~((y <= 1400000.0)))
		tmp = a * (x * b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.05e-5], N[Not[LessEqual[y, 1400000.0]], $MachinePrecision]], N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.04999999999999994e-5 or 1.4e6 < y

   1. Initial program 97.2%

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

   3. Taylor expanded in b around inf 30.9%

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

      1. mul-1-neg 30.9%

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

      2. distribute-rgt-neg-out 30.9%

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

   5. Simplified 30.9%

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

   6. Taylor expanded in a around 0 11.4%

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

      1. mul-1-neg 11.4%

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

      2. unsub-neg 11.4%

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

   8. Simplified 11.4%

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

   9. Taylor expanded in a around inf 20.6%

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

       1. mul-1-neg 20.6%

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

       2. distribute-rgt-neg-in 20.6%

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

       3. distribute-rgt-neg-in 20.6%

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

   11. Simplified 20.6%

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

       1. add0 20.6%

          \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-x\right)\right) + 0} \]

       2. add-sqr-sqrt 8.1%

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)}\right) + 0 \]

       3. sqrt-unprod 25.2%

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right) + 0 \]

       4. sqr-neg 25.2%

          \[\leadsto a \cdot \left(b \cdot \sqrt{\color{blue}{x \cdot x}}\right) + 0 \]

       5. sqrt-unprod 9.0%

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}\right) + 0 \]

       6. add-sqr-sqrt 14.9%

          \[\leadsto a \cdot \left(b \cdot \color{blue}{x}\right) + 0 \]

   13. Applied egg-rr 14.9%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot x\right) + 0} \]
   14. Step-by-step derivation

       1. add0 14.9%

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

   15. Simplified 14.9%

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

   if -1.04999999999999994e-5 < y < 1.4e6

   1. Initial program 94.5%

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

   3. Taylor expanded in b around inf 73.6%

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

      1. mul-1-neg 73.6%

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

      2. distribute-rgt-neg-out 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in a around 0 37.2%

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

4. Final simplification 25.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-5} \lor \neg \left(y \leq 1400000\right):\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 20.1% 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 96.0%

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

3. Taylor expanded in b around inf 50.3%

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

   1. mul-1-neg 50.3%

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

   2. distribute-rgt-neg-out 50.3%

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

5. Simplified 50.3%

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

6. Taylor expanded in a around 0 19.1%

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

7. Final simplification 19.1%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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))))))