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

Percentage Accurate: 96.4% → 99.6%

Time: 16.0s

Alternatives: 15

Speedup: 1.0×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% 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 98.0%

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

   1. fma-def 98.4%

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

   2. sub-neg 98.4%

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

   3. log1p-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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(((a * (log((1.0d0 - z)) - b)) - (y * (t - log(z)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Final simplification 98.0%

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

Alternative 3: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log z - t\\ \mathbf{if}\;y \leq -4 \cdot 10^{+48}:\\ \;\;\;\;x \cdot e^{y \cdot t_1}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+21}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-55} \lor \neg \left(y \leq 1.4 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot {\left(e^{t_1}\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (log z) t)))
   (if (<= y -4e+48)
     (* x (exp (* y t_1)))
     (if (<= y -2.15e+21)
       (* x (exp (* a (- b))))
       (if (or (<= y -1.4e-55) (not (<= y 1.4e-19)))
         (* x (pow (exp t_1) y))
         (* x (exp (* (- a) (+ z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(z) - t;
	double tmp;
	if (y <= -4e+48) {
		tmp = x * exp((y * t_1));
	} else if (y <= -2.15e+21) {
		tmp = x * exp((a * -b));
	} else if ((y <= -1.4e-55) || !(y <= 1.4e-19)) {
		tmp = x * pow(exp(t_1), y);
	} else {
		tmp = x * exp((-a * (z + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(z) - t
    if (y <= (-4d+48)) then
        tmp = x * exp((y * t_1))
    else if (y <= (-2.15d+21)) then
        tmp = x * exp((a * -b))
    else if ((y <= (-1.4d-55)) .or. (.not. (y <= 1.4d-19))) then
        tmp = x * (exp(t_1) ** y)
    else
        tmp = x * exp((-a * (z + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.log(z) - t;
	double tmp;
	if (y <= -4e+48) {
		tmp = x * Math.exp((y * t_1));
	} else if (y <= -2.15e+21) {
		tmp = x * Math.exp((a * -b));
	} else if ((y <= -1.4e-55) || !(y <= 1.4e-19)) {
		tmp = x * Math.pow(Math.exp(t_1), y);
	} else {
		tmp = x * Math.exp((-a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(z) - t
	tmp = 0
	if y <= -4e+48:
		tmp = x * math.exp((y * t_1))
	elif y <= -2.15e+21:
		tmp = x * math.exp((a * -b))
	elif (y <= -1.4e-55) or not (y <= 1.4e-19):
		tmp = x * math.pow(math.exp(t_1), y)
	else:
		tmp = x * math.exp((-a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(z) - t)
	tmp = 0.0
	if (y <= -4e+48)
		tmp = Float64(x * exp(Float64(y * t_1)));
	elseif (y <= -2.15e+21)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif ((y <= -1.4e-55) || !(y <= 1.4e-19))
		tmp = Float64(x * (exp(t_1) ^ y));
	else
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(z) - t;
	tmp = 0.0;
	if (y <= -4e+48)
		tmp = x * exp((y * t_1));
	elseif (y <= -2.15e+21)
		tmp = x * exp((a * -b));
	elseif ((y <= -1.4e-55) || ~((y <= 1.4e-19)))
		tmp = x * (exp(t_1) ^ y);
	else
		tmp = x * exp((-a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[y, -4e+48], N[(x * N[Exp[N[(y * t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e+21], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.4e-55], N[Not[LessEqual[y, 1.4e-19]], $MachinePrecision]], N[(x * N[Power[N[Exp[t$95$1], $MachinePrecision], y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.00000000000000018e48

   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. Taylor expanded in y around inf 86.9%

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

   if -4.00000000000000018e48 < y < -2.15e21

   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. Taylor expanded in b around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

   4. Simplified 100.0%

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

   if -2.15e21 < y < -1.39999999999999992e-55 or 1.40000000000000001e-19 < 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. Taylor expanded in a around 0 89.6%

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

      1. exp-prod 89.6%

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

   4. Simplified 89.6%

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

   if -1.39999999999999992e-55 < y < 1.40000000000000001e-19

   1. Initial program 98.1%

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

   2. Taylor expanded in y around 0 88.9%

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

      1. sub-neg 88.9%

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

      2. +-commutative 88.9%

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

      3. sub-neg 88.9%

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

      4. neg-mul-1 88.9%

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

      5. log1p-def 91.6%

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

      6. neg-mul-1 91.6%

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

      7. +-commutative 91.6%

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

      8. sub-neg 91.6%

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

   4. Simplified 91.6%

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

   5. Taylor expanded in z around 0 91.6%

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

      1. associate-*r* 91.6%

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

      2. associate-*r* 91.6%

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

      3. distribute-lft-out 91.6%

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

      4. neg-mul-1 91.6%

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

   7. Simplified 91.6%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+48}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+21}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-55} \lor \neg \left(y \leq 1.4 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot {\left(e^{\log z - t}\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]

Alternative 4: 74.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ t_2 := y \cdot \left(-t\right)\\ t_3 := x \cdot {z}^{y}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot e^{t_2}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-288}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-101}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot {e}^{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* a (- (- z) b)))))
        (t_2 (* y (- t)))
        (t_3 (* x (pow z y))))
   (if (<= t -9e+69)
     (* x (exp t_2))
     (if (<= t -1.8e-239)
       t_1
       (if (<= t -8.5e-288)
         t_3
         (if (<= t 2.6e-166)
           t_1
           (if (<= t 1.65e-101)
             t_3
             (if (<= t 6.1e+26) t_1 (* x (pow E t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((a * (-z - b)));
	double t_2 = y * -t;
	double t_3 = x * pow(z, y);
	double tmp;
	if (t <= -9e+69) {
		tmp = x * exp(t_2);
	} else if (t <= -1.8e-239) {
		tmp = t_1;
	} else if (t <= -8.5e-288) {
		tmp = t_3;
	} else if (t <= 2.6e-166) {
		tmp = t_1;
	} else if (t <= 1.65e-101) {
		tmp = t_3;
	} else if (t <= 6.1e+26) {
		tmp = t_1;
	} else {
		tmp = x * pow(((double) M_E), t_2);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((a * (-z - b)));
	double t_2 = y * -t;
	double t_3 = x * Math.pow(z, y);
	double tmp;
	if (t <= -9e+69) {
		tmp = x * Math.exp(t_2);
	} else if (t <= -1.8e-239) {
		tmp = t_1;
	} else if (t <= -8.5e-288) {
		tmp = t_3;
	} else if (t <= 2.6e-166) {
		tmp = t_1;
	} else if (t <= 1.65e-101) {
		tmp = t_3;
	} else if (t <= 6.1e+26) {
		tmp = t_1;
	} else {
		tmp = x * Math.pow(Math.E, t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((a * (-z - b)))
	t_2 = y * -t
	t_3 = x * math.pow(z, y)
	tmp = 0
	if t <= -9e+69:
		tmp = x * math.exp(t_2)
	elif t <= -1.8e-239:
		tmp = t_1
	elif t <= -8.5e-288:
		tmp = t_3
	elif t <= 2.6e-166:
		tmp = t_1
	elif t <= 1.65e-101:
		tmp = t_3
	elif t <= 6.1e+26:
		tmp = t_1
	else:
		tmp = x * math.pow(math.e, t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))))
	t_2 = Float64(y * Float64(-t))
	t_3 = Float64(x * (z ^ y))
	tmp = 0.0
	if (t <= -9e+69)
		tmp = Float64(x * exp(t_2));
	elseif (t <= -1.8e-239)
		tmp = t_1;
	elseif (t <= -8.5e-288)
		tmp = t_3;
	elseif (t <= 2.6e-166)
		tmp = t_1;
	elseif (t <= 1.65e-101)
		tmp = t_3;
	elseif (t <= 6.1e+26)
		tmp = t_1;
	else
		tmp = Float64(x * (exp(1) ^ t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((a * (-z - b)));
	t_2 = y * -t;
	t_3 = x * (z ^ y);
	tmp = 0.0;
	if (t <= -9e+69)
		tmp = x * exp(t_2);
	elseif (t <= -1.8e-239)
		tmp = t_1;
	elseif (t <= -8.5e-288)
		tmp = t_3;
	elseif (t <= 2.6e-166)
		tmp = t_1;
	elseif (t <= 1.65e-101)
		tmp = t_3;
	elseif (t <= 6.1e+26)
		tmp = t_1;
	else
		tmp = x * (2.71828182845904523536 ^ 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 * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-t)), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+69], N[(x * N[Exp[t$95$2], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.8e-239], t$95$1, If[LessEqual[t, -8.5e-288], t$95$3, If[LessEqual[t, 2.6e-166], t$95$1, If[LessEqual[t, 1.65e-101], t$95$3, If[LessEqual[t, 6.1e+26], t$95$1, N[(x * N[Power[E, t$95$2], $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.9999999999999999e69

   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 88.6%

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

      1. mul-1-neg 88.6%

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

      2. distribute-rgt-neg-out 88.6%

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

   4. Simplified 88.6%

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

   if -8.9999999999999999e69 < t < -1.8000000000000001e-239 or -8.4999999999999997e-288 < t < 2.59999999999999989e-166 or 1.64999999999999992e-101 < t < 6.1000000000000003e26

   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 0 76.9%

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

      1. sub-neg 76.9%

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

      2. +-commutative 76.9%

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

      3. sub-neg 76.9%

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

      4. neg-mul-1 76.9%

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

      5. log1p-def 80.5%

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

      6. neg-mul-1 80.5%

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

      7. +-commutative 80.5%

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

      8. sub-neg 80.5%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in z around 0 80.5%

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

      1. associate-*r* 80.5%

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

      2. associate-*r* 80.5%

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

      3. distribute-lft-out 80.5%

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

      4. neg-mul-1 80.5%

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

   7. Simplified 80.5%

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

   if -1.8000000000000001e-239 < t < -8.4999999999999997e-288 or 2.59999999999999989e-166 < t < 1.64999999999999992e-101

   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. Taylor expanded in y around inf 95.8%

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

   3. Taylor expanded in t around 0 95.8%

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

   if 6.1000000000000003e26 < t

   1. Initial program 98.0%

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

      1. *-un-lft-identity 98.0%

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

      2. exp-prod 98.1%

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

      3. exp-1-e 98.1%

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

      4. fma-def 98.1%

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

      5. sub-neg 98.1%

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

      6. sub-neg 98.1%

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

      7. log1p-udef 99.9%

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

      8. sub-neg 99.9%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 94.6%

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

      11. sqr-neg 94.6%

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

      12. sqrt-unprod 94.6%

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

      13. add-sqr-sqrt 94.6%

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

   3. Applied egg-rr 94.6%

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

   4. Taylor expanded in t around inf 85.9%

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

      1. mul-1-neg 85.9%

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

      2. *-commutative 85.9%

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

      3. distribute-rgt-neg-in 85.9%

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

   6. Simplified 85.9%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-239}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-288}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-166}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-101}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+26}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {e}^{\left(y \cdot \left(-t\right)\right)}\\ \end{array} \]

Alternative 5: 86.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-56} \lor \neg \left(y \leq 3.8 \cdot 10^{-22}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* y (- (log z) t))))))
   (if (<= y -4e+48)
     t_1
     (if (<= y -6.2e+21)
       (* x (exp (* a (- b))))
       (if (or (<= y -2e-56) (not (<= y 3.8e-22)))
         t_1
         (* x (exp (* (- a) (+ z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((y * (log(z) - t)));
	double tmp;
	if (y <= -4e+48) {
		tmp = t_1;
	} else if (y <= -6.2e+21) {
		tmp = x * exp((a * -b));
	} else if ((y <= -2e-56) || !(y <= 3.8e-22)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * exp((y * (log(z) - t)))
    if (y <= (-4d+48)) then
        tmp = t_1
    else if (y <= (-6.2d+21)) then
        tmp = x * exp((a * -b))
    else if ((y <= (-2d-56)) .or. (.not. (y <= 3.8d-22))) then
        tmp = t_1
    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 t_1 = x * Math.exp((y * (Math.log(z) - t)));
	double tmp;
	if (y <= -4e+48) {
		tmp = t_1;
	} else if (y <= -6.2e+21) {
		tmp = x * Math.exp((a * -b));
	} else if ((y <= -2e-56) || !(y <= 3.8e-22)) {
		tmp = t_1;
	} else {
		tmp = x * Math.exp((-a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((y * (math.log(z) - t)))
	tmp = 0
	if y <= -4e+48:
		tmp = t_1
	elif y <= -6.2e+21:
		tmp = x * math.exp((a * -b))
	elif (y <= -2e-56) or not (y <= 3.8e-22):
		tmp = t_1
	else:
		tmp = x * math.exp((-a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(y * Float64(log(z) - t))))
	tmp = 0.0
	if (y <= -4e+48)
		tmp = t_1;
	elseif (y <= -6.2e+21)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif ((y <= -2e-56) || !(y <= 3.8e-22))
		tmp = t_1;
	else
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((y * (log(z) - t)));
	tmp = 0.0;
	if (y <= -4e+48)
		tmp = t_1;
	elseif (y <= -6.2e+21)
		tmp = x * exp((a * -b));
	elseif ((y <= -2e-56) || ~((y <= 3.8e-22)))
		tmp = t_1;
	else
		tmp = x * exp((-a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+48], t$95$1, If[LessEqual[y, -6.2e+21], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2e-56], N[Not[LessEqual[y, 3.8e-22]], $MachinePrecision]], t$95$1, N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.00000000000000018e48 or -6.2e21 < y < -2.0000000000000001e-56 or 3.80000000000000023e-22 < y

   1. Initial program 97.9%

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

   2. Taylor expanded in y around inf 88.7%

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

   if -4.00000000000000018e48 < y < -6.2e21

   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. Taylor expanded in b around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

   4. Simplified 100.0%

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

   if -2.0000000000000001e-56 < y < 3.80000000000000023e-22

   1. Initial program 98.1%

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

   2. Taylor expanded in y around 0 88.9%

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

      1. sub-neg 88.9%

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

      2. +-commutative 88.9%

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

      3. sub-neg 88.9%

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

      4. neg-mul-1 88.9%

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

      5. log1p-def 91.6%

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

      6. neg-mul-1 91.6%

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

      7. +-commutative 91.6%

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

      8. sub-neg 91.6%

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

   4. Simplified 91.6%

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

   5. Taylor expanded in z around 0 91.6%

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

      1. associate-*r* 91.6%

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

      2. associate-*r* 91.6%

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

      3. distribute-lft-out 91.6%

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

      4. neg-mul-1 91.6%

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

   7. Simplified 91.6%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+48}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-56} \lor \neg \left(y \leq 3.8 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]

Alternative 6: 74.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ t_2 := x \cdot e^{y \cdot \left(-t\right)}\\ t_3 := x \cdot {z}^{y}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-293}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-101}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* a (- (- z) b)))))
        (t_2 (* x (exp (* y (- t)))))
        (t_3 (* x (pow z y))))
   (if (<= t -7e+68)
     t_2
     (if (<= t -1.7e-239)
       t_1
       (if (<= t -3.1e-293)
         t_3
         (if (<= t 8.8e-166)
           t_1
           (if (<= t 1.7e-101) t_3 (if (<= t 1.15e+33) 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 * (-z - b)));
	double t_2 = x * exp((y * -t));
	double t_3 = x * pow(z, y);
	double tmp;
	if (t <= -7e+68) {
		tmp = t_2;
	} else if (t <= -1.7e-239) {
		tmp = t_1;
	} else if (t <= -3.1e-293) {
		tmp = t_3;
	} else if (t <= 8.8e-166) {
		tmp = t_1;
	} else if (t <= 1.7e-101) {
		tmp = t_3;
	} else if (t <= 1.15e+33) {
		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 * (-z - b)))
    t_2 = x * exp((y * -t))
    t_3 = x * (z ** y)
    if (t <= (-7d+68)) then
        tmp = t_2
    else if (t <= (-1.7d-239)) then
        tmp = t_1
    else if (t <= (-3.1d-293)) then
        tmp = t_3
    else if (t <= 8.8d-166) then
        tmp = t_1
    else if (t <= 1.7d-101) then
        tmp = t_3
    else if (t <= 1.15d+33) 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 * (-z - b)));
	double t_2 = x * Math.exp((y * -t));
	double t_3 = x * Math.pow(z, y);
	double tmp;
	if (t <= -7e+68) {
		tmp = t_2;
	} else if (t <= -1.7e-239) {
		tmp = t_1;
	} else if (t <= -3.1e-293) {
		tmp = t_3;
	} else if (t <= 8.8e-166) {
		tmp = t_1;
	} else if (t <= 1.7e-101) {
		tmp = t_3;
	} else if (t <= 1.15e+33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((a * (-z - b)))
	t_2 = x * math.exp((y * -t))
	t_3 = x * math.pow(z, y)
	tmp = 0
	if t <= -7e+68:
		tmp = t_2
	elif t <= -1.7e-239:
		tmp = t_1
	elif t <= -3.1e-293:
		tmp = t_3
	elif t <= 8.8e-166:
		tmp = t_1
	elif t <= 1.7e-101:
		tmp = t_3
	elif t <= 1.15e+33:
		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(Float64(-z) - b))))
	t_2 = Float64(x * exp(Float64(y * Float64(-t))))
	t_3 = Float64(x * (z ^ y))
	tmp = 0.0
	if (t <= -7e+68)
		tmp = t_2;
	elseif (t <= -1.7e-239)
		tmp = t_1;
	elseif (t <= -3.1e-293)
		tmp = t_3;
	elseif (t <= 8.8e-166)
		tmp = t_1;
	elseif (t <= 1.7e-101)
		tmp = t_3;
	elseif (t <= 1.15e+33)
		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 * (-z - b)));
	t_2 = x * exp((y * -t));
	t_3 = x * (z ^ y);
	tmp = 0.0;
	if (t <= -7e+68)
		tmp = t_2;
	elseif (t <= -1.7e-239)
		tmp = t_1;
	elseif (t <= -3.1e-293)
		tmp = t_3;
	elseif (t <= 8.8e-166)
		tmp = t_1;
	elseif (t <= 1.7e-101)
		tmp = t_3;
	elseif (t <= 1.15e+33)
		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 * N[((-z) - b), $MachinePrecision]), $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, -7e+68], t$95$2, If[LessEqual[t, -1.7e-239], t$95$1, If[LessEqual[t, -3.1e-293], t$95$3, If[LessEqual[t, 8.8e-166], t$95$1, If[LessEqual[t, 1.7e-101], t$95$3, If[LessEqual[t, 1.15e+33], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.99999999999999955e68 or 1.15000000000000005e33 < t

   1. Initial program 97.9%

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

   2. Taylor expanded in t around inf 87.0%

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

      1. mul-1-neg 87.0%

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

      2. distribute-rgt-neg-out 87.0%

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

   4. Simplified 87.0%

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

   if -6.99999999999999955e68 < t < -1.7e-239 or -3.09999999999999983e-293 < t < 8.8000000000000005e-166 or 1.69999999999999995e-101 < t < 1.15000000000000005e33

   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 0 76.9%

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

      1. sub-neg 76.9%

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

      2. +-commutative 76.9%

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

      3. sub-neg 76.9%

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

      4. neg-mul-1 76.9%

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

      5. log1p-def 80.5%

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

      6. neg-mul-1 80.5%

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

      7. +-commutative 80.5%

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

      8. sub-neg 80.5%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in z around 0 80.5%

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

      1. associate-*r* 80.5%

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

      2. associate-*r* 80.5%

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

      3. distribute-lft-out 80.5%

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

      4. neg-mul-1 80.5%

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

   7. Simplified 80.5%

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

   if -1.7e-239 < t < -3.09999999999999983e-293 or 8.8000000000000005e-166 < t < 1.69999999999999995e-101

   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. Taylor expanded in y around inf 95.8%

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

   3. Taylor expanded in t around 0 95.8%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+68}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-239}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-293}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-166}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-101}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+33}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 7: 71.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+48} \lor \neg \left(y \leq 7.2 \cdot 10^{+114}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.2e+48) (not (<= y 7.2e+114)))
   (* 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 <= -6.2e+48) || !(y <= 7.2e+114)) {
		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 <= (-6.2d+48)) .or. (.not. (y <= 7.2d+114))) 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 <= -6.2e+48) || !(y <= 7.2e+114)) {
		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 <= -6.2e+48) or not (y <= 7.2e+114):
		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 <= -6.2e+48) || !(y <= 7.2e+114))
		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 <= -6.2e+48) || ~((y <= 7.2e+114)))
		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, -6.2e+48], N[Not[LessEqual[y, 7.2e+114]], $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 < -6.20000000000000011e48 or 7.2000000000000001e114 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 88.8%

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

   3. Taylor expanded in t around 0 69.8%

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

   if -6.20000000000000011e48 < y < 7.2000000000000001e114

   1. Initial program 97.0%

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

   2. Taylor expanded in b around inf 77.9%

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

      1. associate-*r* 77.9%

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

      2. *-commutative 77.9%

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

      3. neg-mul-1 77.9%

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

   4. Simplified 77.9%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+48} \lor \neg \left(y \leq 7.2 \cdot 10^{+114}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 8: 70.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+27} \lor \neg \left(b \leq 6.8 \cdot 10^{+68}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.75e+27) (not (<= b 6.8e+68)))
   (* x (exp (* a (- b))))
   (* x (exp (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.75e+27) || !(b <= 6.8e+68)) {
		tmp = x * exp((a * -b));
	} else {
		tmp = x * exp((y * -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 ((b <= (-1.75d+27)) .or. (.not. (b <= 6.8d+68))) then
        tmp = x * exp((a * -b))
    else
        tmp = x * exp((y * -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 ((b <= -1.75e+27) || !(b <= 6.8e+68)) {
		tmp = x * Math.exp((a * -b));
	} else {
		tmp = x * Math.exp((y * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.75e+27) or not (b <= 6.8e+68):
		tmp = x * math.exp((a * -b))
	else:
		tmp = x * math.exp((y * -t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.75e+27) || !(b <= 6.8e+68))
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	else
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.75e+27) || ~((b <= 6.8e+68)))
		tmp = x * exp((a * -b));
	else
		tmp = x * exp((y * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.75e+27], N[Not[LessEqual[b, 6.8e+68]], $MachinePrecision]], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7500000000000001e27 or 6.8000000000000003e68 < b

   1. Initial program 99.1%

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

   2. Taylor expanded in b around inf 81.3%

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

      1. associate-*r* 81.3%

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

      2. *-commutative 81.3%

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

      3. neg-mul-1 81.3%

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

   4. Simplified 81.3%

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

   if -1.7500000000000001e27 < b < 6.8000000000000003e68

   1. Initial program 97.3%

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

   2. Taylor expanded in t around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-rgt-neg-out 70.8%

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

   4. Simplified 70.8%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+27} \lor \neg \left(b \leq 6.8 \cdot 10^{+68}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 9: 54.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.2e+34) (- x (* x (* 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 <= -3.2e+34) {
		tmp = x - (x * (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 <= (-3.2d+34)) then
        tmp = x - (x * (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 <= -3.2e+34) {
		tmp = x - (x * (y * t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.2e+34:
		tmp = x - (x * (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 <= -3.2e+34)
		tmp = Float64(x - Float64(x * 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 <= -3.2e+34)
		tmp = x - (x * (y * t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.2e+34], N[(x - N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1999999999999998e34

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf 81.9%

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

      1. mul-1-neg 81.9%

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

      2. distribute-rgt-neg-out 81.9%

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

   4. Simplified 81.9%

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

   5. Taylor expanded in y around 0 34.2%

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

   6. Taylor expanded in x around 0 34.2%

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

      1. *-commutative 34.2%

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

      2. mul-1-neg 34.2%

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

      3. +-commutative 34.2%

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

      4. distribute-lft-in 34.2%

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

      5. *-rgt-identity 34.2%

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

      6. distribute-rgt-neg-in 34.2%

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

      7. sub-neg 34.2%

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

   8. Simplified 34.2%

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

   if -3.1999999999999998e34 < t

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 71.2%

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

   3. Taylor expanded in t around 0 61.0%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 10: 33.6% accurate, 16.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{x \cdot a}{\frac{b - z}{b \cdot b - z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 6.2e-63)
   (- x (/ (* x a) (/ (- b z) (- (* b b) (* z z)))))
   (* x (* z (- a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.2e-63) {
		tmp = x - ((x * a) / ((b - z) / ((b * b) - (z * z))));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 6.2d-63) then
        tmp = x - ((x * a) / ((b - z) / ((b * b) - (z * z))))
    else
        tmp = x * (z * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.2e-63) {
		tmp = x - ((x * a) / ((b - z) / ((b * b) - (z * z))));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 6.2e-63:
		tmp = x - ((x * a) / ((b - z) / ((b * b) - (z * z))))
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 6.2e-63)
		tmp = Float64(x - Float64(Float64(x * a) / Float64(Float64(b - z) / Float64(Float64(b * b) - Float64(z * z)))));
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 6.2e-63)
		tmp = x - ((x * a) / ((b - z) / ((b * b) - (z * z))));
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 6.2e-63], N[(x - N[(N[(x * a), $MachinePrecision] / N[(N[(b - z), $MachinePrecision] / N[(N[(b * b), $MachinePrecision] - N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.19999999999999968e-63

   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 y around 0 72.2%

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

      1. sub-neg 72.2%

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

      2. +-commutative 72.2%

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

      3. sub-neg 72.2%

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

      4. neg-mul-1 72.2%

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

      5. log1p-def 74.4%

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

      6. neg-mul-1 74.4%

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

      7. +-commutative 74.4%

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

      8. sub-neg 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in z around 0 74.4%

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

      1. associate-*r* 74.4%

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

      2. associate-*r* 74.4%

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

      3. distribute-lft-out 74.4%

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

      4. neg-mul-1 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in a around 0 34.9%

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

      1. +-commutative 34.9%

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

      2. mul-1-neg 34.9%

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

      3. unsub-neg 34.9%

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

      4. associate-*r* 35.4%

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

      5. *-commutative 35.4%

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

      6. +-commutative 35.4%

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

   10. Simplified 35.4%

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

       1. *-commutative 35.4%

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

       2. flip-+ 39.5%

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

       3. associate-*r/ 40.0%

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

   12. Applied egg-rr 40.0%

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

       1. associate-/l* 39.5%

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

   14. Simplified 39.5%

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

   if 6.19999999999999968e-63 < y

   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. Taylor expanded in y around 0 40.6%

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

      1. sub-neg 40.6%

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

      2. +-commutative 40.6%

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

      3. sub-neg 40.6%

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

      4. neg-mul-1 40.6%

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

      5. log1p-def 44.1%

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

      6. neg-mul-1 44.1%

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

      7. +-commutative 44.1%

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

      8. sub-neg 44.1%

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

   4. Simplified 44.1%

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

   5. Taylor expanded in z around 0 44.1%

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

      1. associate-*r* 44.1%

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

      2. associate-*r* 44.1%

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

      3. distribute-lft-out 44.1%

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

      4. neg-mul-1 44.1%

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

   7. Simplified 44.1%

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

   8. Taylor expanded in a around 0 8.9%

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

      1. +-commutative 8.9%

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

      2. mul-1-neg 8.9%

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

      3. unsub-neg 8.9%

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

      4. associate-*r* 8.9%

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

      5. *-commutative 8.9%

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

      6. +-commutative 8.9%

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

   10. Simplified 8.9%

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

   11. Taylor expanded in z around inf 27.5%

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

       1. mul-1-neg 27.5%

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

       2. associate-*r* 29.7%

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

       3. *-commutative 29.7%

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

   13. Simplified 29.7%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{x \cdot a}{\frac{b - z}{b \cdot b - z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 11: 34.2% accurate, 16.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{\left(x \cdot a\right) \cdot \left(z \cdot z - b \cdot b\right)}{b - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 6.2e-63)
   (+ x (/ (* (* x a) (- (* z z) (* b b))) (- b z)))
   (* x (* z (- a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.2e-63) {
		tmp = x + (((x * a) * ((z * z) - (b * b))) / (b - z));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 6.2d-63) then
        tmp = x + (((x * a) * ((z * z) - (b * b))) / (b - z))
    else
        tmp = x * (z * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.2e-63) {
		tmp = x + (((x * a) * ((z * z) - (b * b))) / (b - z));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 6.2e-63:
		tmp = x + (((x * a) * ((z * z) - (b * b))) / (b - z))
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 6.2e-63)
		tmp = Float64(x + Float64(Float64(Float64(x * a) * Float64(Float64(z * z) - Float64(b * b))) / Float64(b - z)));
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 6.2e-63)
		tmp = x + (((x * a) * ((z * z) - (b * b))) / (b - z));
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 6.2e-63], N[(x + N[(N[(N[(x * a), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] - N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.19999999999999968e-63

   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 y around 0 72.2%

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

      1. sub-neg 72.2%

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

      2. +-commutative 72.2%

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

      3. sub-neg 72.2%

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

      4. neg-mul-1 72.2%

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

      5. log1p-def 74.4%

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

      6. neg-mul-1 74.4%

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

      7. +-commutative 74.4%

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

      8. sub-neg 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in z around 0 74.4%

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

      1. associate-*r* 74.4%

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

      2. associate-*r* 74.4%

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

      3. distribute-lft-out 74.4%

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

      4. neg-mul-1 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in a around 0 34.9%

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

      1. +-commutative 34.9%

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

      2. mul-1-neg 34.9%

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

      3. unsub-neg 34.9%

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

      4. associate-*r* 35.4%

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

      5. *-commutative 35.4%

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

      6. +-commutative 35.4%

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

   10. Simplified 35.4%

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

       1. flip-+ 39.5%

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

       2. associate-*l/ 40.0%

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

   12. Applied egg-rr 40.0%

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

   if 6.19999999999999968e-63 < y

   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. Taylor expanded in y around 0 40.6%

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

      1. sub-neg 40.6%

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

      2. +-commutative 40.6%

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

      3. sub-neg 40.6%

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

      4. neg-mul-1 40.6%

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

      5. log1p-def 44.1%

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

      6. neg-mul-1 44.1%

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

      7. +-commutative 44.1%

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

      8. sub-neg 44.1%

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

   4. Simplified 44.1%

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

   5. Taylor expanded in z around 0 44.1%

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

      1. associate-*r* 44.1%

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

      2. associate-*r* 44.1%

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

      3. distribute-lft-out 44.1%

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

      4. neg-mul-1 44.1%

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

   7. Simplified 44.1%

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

   8. Taylor expanded in a around 0 8.9%

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

      1. +-commutative 8.9%

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

      2. mul-1-neg 8.9%

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

      3. unsub-neg 8.9%

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

      4. associate-*r* 8.9%

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

      5. *-commutative 8.9%

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

      6. +-commutative 8.9%

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

   10. Simplified 8.9%

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

   11. Taylor expanded in z around inf 27.5%

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

       1. mul-1-neg 27.5%

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

       2. associate-*r* 29.7%

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

       3. *-commutative 29.7%

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

   13. Simplified 29.7%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{\left(x \cdot a\right) \cdot \left(z \cdot z - b \cdot b\right)}{b - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 12: 27.5% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0205 \lor \neg \left(y \leq 4.7 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.0205) (not (<= y 4.7e-63))) (* x (* z (- a))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.0205) || !(y <= 4.7e-63)) {
		tmp = x * (z * -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 <= (-0.0205d0)) .or. (.not. (y <= 4.7d-63))) then
        tmp = x * (z * -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 <= -0.0205) || !(y <= 4.7e-63)) {
		tmp = x * (z * -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -0.0205) or not (y <= 4.7e-63):
		tmp = x * (z * -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -0.0205) || !(y <= 4.7e-63))
		tmp = Float64(x * Float64(z * 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 <= -0.0205) || ~((y <= 4.7e-63)))
		tmp = x * (z * -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -0.0205], N[Not[LessEqual[y, 4.7e-63]], $MachinePrecision]], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -0.0205000000000000009 or 4.7000000000000001e-63 < 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. Taylor expanded in y around 0 41.4%

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

      1. sub-neg 41.4%

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

      2. +-commutative 41.4%

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

      3. sub-neg 41.4%

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

      4. neg-mul-1 41.4%

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

      5. log1p-def 44.8%

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

      6. neg-mul-1 44.8%

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

      7. +-commutative 44.8%

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

      8. sub-neg 44.8%

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

   4. Simplified 44.8%

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

   5. Taylor expanded in z around 0 44.8%

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

      1. associate-*r* 44.8%

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

      2. associate-*r* 44.8%

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

      3. distribute-lft-out 44.8%

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

      4. neg-mul-1 44.8%

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

   7. Simplified 44.8%

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

   8. Taylor expanded in a around 0 7.8%

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

      1. +-commutative 7.8%

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

      2. mul-1-neg 7.8%

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

      3. unsub-neg 7.8%

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

      4. associate-*r* 7.8%

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

      5. *-commutative 7.8%

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

      6. +-commutative 7.8%

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

   10. Simplified 7.8%

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

   11. Taylor expanded in z around inf 20.5%

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

       1. mul-1-neg 20.5%

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

       2. associate-*r* 22.0%

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

       3. *-commutative 22.0%

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

   13. Simplified 22.0%

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

   if -0.0205000000000000009 < y < 4.7000000000000001e-63

   1. Initial program 99.1%

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

   2. Taylor expanded in b around inf 86.4%

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

      1. associate-*r* 86.4%

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

      2. *-commutative 86.4%

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

      3. neg-mul-1 86.4%

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

   4. Simplified 86.4%

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

   5. Taylor expanded in b around 0 44.3%

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

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0205 \lor \neg \left(y \leq 4.7 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 29.0% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-24}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.7e-24)
   (* (* y t) (- x))
   (if (<= y 2.3e-63) x (* x (* z (- a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.7e-24) {
		tmp = (y * t) * -x;
	} else if (y <= 2.3e-63) {
		tmp = x;
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.7d-24)) then
        tmp = (y * t) * -x
    else if (y <= 2.3d-63) then
        tmp = x
    else
        tmp = x * (z * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.7e-24) {
		tmp = (y * t) * -x;
	} else if (y <= 2.3e-63) {
		tmp = x;
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.7e-24:
		tmp = (y * t) * -x
	elif y <= 2.3e-63:
		tmp = x
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.7e-24)
		tmp = Float64(Float64(y * t) * Float64(-x));
	elseif (y <= 2.3e-63)
		tmp = x;
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.7e-24)
		tmp = (y * t) * -x;
	elseif (y <= 2.3e-63)
		tmp = x;
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.7e-24], N[(N[(y * t), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[y, 2.3e-63], x, N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.70000000000000007e-24

   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 50.0%

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

      1. mul-1-neg 50.0%

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

      2. distribute-rgt-neg-out 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in y around 0 11.5%

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

   6. Taylor expanded in y around inf 11.2%

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

      1. associate-*r* 11.2%

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

      2. neg-mul-1 11.2%

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

   8. Simplified 11.2%

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

   if -2.70000000000000007e-24 < y < 2.3e-63

   1. Initial program 99.0%

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

   2. Taylor expanded in b around inf 88.7%

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

      1. associate-*r* 88.7%

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

      2. *-commutative 88.7%

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

      3. neg-mul-1 88.7%

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

   4. Simplified 88.7%

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

   5. Taylor expanded in b around 0 47.6%

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

   if 2.3e-63 < y

   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. Taylor expanded in y around 0 40.6%

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

      1. sub-neg 40.6%

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

      2. +-commutative 40.6%

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

      3. sub-neg 40.6%

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

      4. neg-mul-1 40.6%

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

      5. log1p-def 44.1%

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

      6. neg-mul-1 44.1%

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

      7. +-commutative 44.1%

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

      8. sub-neg 44.1%

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

   4. Simplified 44.1%

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

   5. Taylor expanded in z around 0 44.1%

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

      1. associate-*r* 44.1%

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

      2. associate-*r* 44.1%

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

      3. distribute-lft-out 44.1%

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

      4. neg-mul-1 44.1%

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

   7. Simplified 44.1%

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

   8. Taylor expanded in a around 0 8.9%

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

      1. +-commutative 8.9%

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

      2. mul-1-neg 8.9%

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

      3. unsub-neg 8.9%

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

      4. associate-*r* 8.9%

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

      5. *-commutative 8.9%

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

      6. +-commutative 8.9%

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

   10. Simplified 8.9%

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

   11. Taylor expanded in z around inf 27.5%

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

       1. mul-1-neg 27.5%

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

       2. associate-*r* 29.7%

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

       3. *-commutative 29.7%

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

   13. Simplified 29.7%

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

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-24}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 14: 32.1% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 6.2e-63) (* x (- 1.0 (* a b))) (* x (* z (- a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.2e-63) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 6.2d-63) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (z * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.2e-63) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 6.2e-63:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 6.2e-63)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 6.2e-63)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 6.2e-63], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.19999999999999968e-63

   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 71.1%

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

      1. associate-*r* 71.1%

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

      2. *-commutative 71.1%

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

      3. neg-mul-1 71.1%

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

   4. Simplified 71.1%

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

   5. Taylor expanded in b around 0 39.2%

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

      1. mul-1-neg 39.2%

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

      2. unsub-neg 39.2%

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

      3. *-commutative 39.2%

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

   7. Simplified 39.2%

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

   if 6.19999999999999968e-63 < y

   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. Taylor expanded in y around 0 40.6%

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

      1. sub-neg 40.6%

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

      2. +-commutative 40.6%

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

      3. sub-neg 40.6%

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

      4. neg-mul-1 40.6%

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

      5. log1p-def 44.1%

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

      6. neg-mul-1 44.1%

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

      7. +-commutative 44.1%

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

      8. sub-neg 44.1%

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

   4. Simplified 44.1%

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

   5. Taylor expanded in z around 0 44.1%

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

      1. associate-*r* 44.1%

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

      2. associate-*r* 44.1%

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

      3. distribute-lft-out 44.1%

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

      4. neg-mul-1 44.1%

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

   7. Simplified 44.1%

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

   8. Taylor expanded in a around 0 8.9%

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

      1. +-commutative 8.9%

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

      2. mul-1-neg 8.9%

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

      3. unsub-neg 8.9%

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

      4. associate-*r* 8.9%

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

      5. *-commutative 8.9%

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

      6. +-commutative 8.9%

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

   10. Simplified 8.9%

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

   11. Taylor expanded in z around inf 27.5%

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

       1. mul-1-neg 27.5%

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

       2. associate-*r* 29.7%

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

       3. *-commutative 29.7%

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

   13. Simplified 29.7%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 15: 19.5% 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 98.0%

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

2. Taylor expanded in b around inf 61.6%

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

   1. associate-*r* 61.6%

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

   2. *-commutative 61.6%

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

   3. neg-mul-1 61.6%

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

4. Simplified 61.6%

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

5. Taylor expanded in b around 0 22.5%

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

6. Final simplification 22.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023195 
(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))))))