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

Percentage Accurate: 96.6% → 99.5%

Time: 30.7s

Alternatives: 20

Speedup: 1.0×

• 40.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.1%

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

   1. fma-define 95.5%

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

   2. sub-neg 95.5%

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

   3. log1p-define 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.1%

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

3. Final simplification 95.1%

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

Alternative 3: 87.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-24} \lor \neg \left(y \leq 1.8 \cdot 10^{-54}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.85e-24) (not (<= y 1.8e-54)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* (- a) (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.85e-24) || !(y <= 1.8e-54)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((-a * (z + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.85d-24)) .or. (.not. (y <= 1.8d-54))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((-a * (z + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.85e-24) || !(y <= 1.8e-54)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((-a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.85e-24) or not (y <= 1.8e-54):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((-a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.85e-24) || !(y <= 1.8e-54))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.85e-24) || ~((y <= 1.8e-54)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((-a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.85e-24], N[Not[LessEqual[y, 1.8e-54]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.85000000000000001e-24 or 1.79999999999999988e-54 < y

   1. Initial program 99.3%

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

   3. Taylor expanded in y around inf 87.6%

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

   if -2.85000000000000001e-24 < y < 1.79999999999999988e-54

   1. Initial program 89.7%

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

   3. Taylor expanded in y around 0 81.6%

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

      1. sub-neg 81.6%

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

      2. log1p-define 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in z around 0 90.9%

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

      1. associate-*r* 90.9%

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

      2. associate-*r* 90.9%

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

      3. distribute-lft-out 90.9%

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

      4. mul-1-neg 90.9%

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

   8. Simplified 90.9%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-24} \lor \neg \left(y \leq 1.8 \cdot 10^{-54}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{a \cdot \left(-b\right)}\\ t_2 := e^{y \cdot \left(-t\right)}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-195}:\\ \;\;\;\;x - y \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-68}:\\ \;\;\;\;x - x \cdot \left(a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (exp (* a (- b)))) (t_2 (exp (* y (- t)))))
   (if (<= y -1.75e-31)
     t_2
     (if (<= y -8.5e-118)
       t_1
       (if (<= y -9.2e-195)
         (- x (* y (* x t)))
         (if (<= y -7.5e-274)
           t_1
           (if (<= y 2.25e-68) (- x (* x (* a (+ z b)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp((a * -b));
	double t_2 = exp((y * -t));
	double tmp;
	if (y <= -1.75e-31) {
		tmp = t_2;
	} else if (y <= -8.5e-118) {
		tmp = t_1;
	} else if (y <= -9.2e-195) {
		tmp = x - (y * (x * t));
	} else if (y <= -7.5e-274) {
		tmp = t_1;
	} else if (y <= 2.25e-68) {
		tmp = x - (x * (a * (z + b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = exp((a * -b))
    t_2 = exp((y * -t))
    if (y <= (-1.75d-31)) then
        tmp = t_2
    else if (y <= (-8.5d-118)) then
        tmp = t_1
    else if (y <= (-9.2d-195)) then
        tmp = x - (y * (x * t))
    else if (y <= (-7.5d-274)) then
        tmp = t_1
    else if (y <= 2.25d-68) then
        tmp = x - (x * (a * (z + b)))
    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 = Math.exp((a * -b));
	double t_2 = Math.exp((y * -t));
	double tmp;
	if (y <= -1.75e-31) {
		tmp = t_2;
	} else if (y <= -8.5e-118) {
		tmp = t_1;
	} else if (y <= -9.2e-195) {
		tmp = x - (y * (x * t));
	} else if (y <= -7.5e-274) {
		tmp = t_1;
	} else if (y <= 2.25e-68) {
		tmp = x - (x * (a * (z + b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp((a * -b))
	t_2 = math.exp((y * -t))
	tmp = 0
	if y <= -1.75e-31:
		tmp = t_2
	elif y <= -8.5e-118:
		tmp = t_1
	elif y <= -9.2e-195:
		tmp = x - (y * (x * t))
	elif y <= -7.5e-274:
		tmp = t_1
	elif y <= 2.25e-68:
		tmp = x - (x * (a * (z + b)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = exp(Float64(a * Float64(-b)))
	t_2 = exp(Float64(y * Float64(-t)))
	tmp = 0.0
	if (y <= -1.75e-31)
		tmp = t_2;
	elseif (y <= -8.5e-118)
		tmp = t_1;
	elseif (y <= -9.2e-195)
		tmp = Float64(x - Float64(y * Float64(x * t)));
	elseif (y <= -7.5e-274)
		tmp = t_1;
	elseif (y <= 2.25e-68)
		tmp = Float64(x - Float64(x * Float64(a * Float64(z + b))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp((a * -b));
	t_2 = exp((y * -t));
	tmp = 0.0;
	if (y <= -1.75e-31)
		tmp = t_2;
	elseif (y <= -8.5e-118)
		tmp = t_1;
	elseif (y <= -9.2e-195)
		tmp = x - (y * (x * t));
	elseif (y <= -7.5e-274)
		tmp = t_1;
	elseif (y <= 2.25e-68)
		tmp = x - (x * (a * (z + b)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -1.75e-31], t$95$2, If[LessEqual[y, -8.5e-118], t$95$1, If[LessEqual[y, -9.2e-195], N[(x - N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-274], t$95$1, If[LessEqual[y, 2.25e-68], N[(x - N[(x * N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.74999999999999993e-31 or 2.25e-68 < y

   1. Initial program 99.3%

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

      1. add-exp-log 70.8%

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

      2. *-commutative 70.8%

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

      3. log-prod 42.4%

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

   4. Applied egg-rr 42.4%

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

   5. Taylor expanded in t around inf 44.1%

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

      1. associate-*r* 44.1%

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

      2. mul-1-neg 44.1%

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

   7. Simplified 44.1%

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

   if -1.74999999999999993e-31 < y < -8.50000000000000087e-118 or -9.2000000000000007e-195 < y < -7.49999999999999968e-274

   1. Initial program 88.0%

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

      1. add-exp-log 62.5%

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

      2. *-commutative 62.5%

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

      3. log-prod 40.6%

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

   4. Applied egg-rr 40.3%

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

   5. Taylor expanded in b around inf 54.1%

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

      1. associate-*r* 54.1%

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

      2. neg-mul-1 54.1%

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

   7. Simplified 54.1%

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

   if -8.50000000000000087e-118 < y < -9.2000000000000007e-195

   1. Initial program 91.2%

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

   3. Taylor expanded in t around inf 82.7%

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

      1. mul-1-neg 82.7%

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

      2. distribute-lft-neg-out 82.7%

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

      3. *-commutative 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. unsub-neg 65.2%

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

      3. associate-*r* 73.8%

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

      4. *-commutative 73.8%

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

   8. Simplified 73.8%

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

   if -7.49999999999999968e-274 < y < 2.25e-68

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0 82.8%

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

      1. sub-neg 82.8%

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

      2. log1p-define 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in z around 0 91.7%

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

      1. associate-*r* 91.7%

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

      2. associate-*r* 91.7%

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

      3. distribute-lft-out 91.7%

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

      4. mul-1-neg 91.7%

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

   8. Simplified 91.7%

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

   9. Taylor expanded in a around 0 55.8%

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

       1. mul-1-neg 55.8%

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

       2. unsub-neg 55.8%

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

       3. *-commutative 55.8%

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

       4. associate-*l* 57.3%

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

       5. *-commutative 57.3%

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

   11. Simplified 57.3%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-31}:\\ \;\;\;\;e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-118}:\\ \;\;\;\;e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-195}:\\ \;\;\;\;x - y \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-274}:\\ \;\;\;\;e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-68}:\\ \;\;\;\;x - x \cdot \left(a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ t_2 := e^{y \cdot \left(-t\right)}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-266}:\\ \;\;\;\;e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))) (t_2 (exp (* y (- t)))))
   (if (<= t -5e+25)
     t_2
     (if (<= t -2.15e-191)
       t_1
       (if (<= t 1.6e-266) (exp (* a (- b))) (if (<= t 1.22e+87) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double t_2 = exp((y * -t));
	double tmp;
	if (t <= -5e+25) {
		tmp = t_2;
	} else if (t <= -2.15e-191) {
		tmp = t_1;
	} else if (t <= 1.6e-266) {
		tmp = exp((a * -b));
	} else if (t <= 1.22e+87) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z ** y)
    t_2 = exp((y * -t))
    if (t <= (-5d+25)) then
        tmp = t_2
    else if (t <= (-2.15d-191)) then
        tmp = t_1
    else if (t <= 1.6d-266) then
        tmp = exp((a * -b))
    else if (t <= 1.22d+87) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double t_2 = Math.exp((y * -t));
	double tmp;
	if (t <= -5e+25) {
		tmp = t_2;
	} else if (t <= -2.15e-191) {
		tmp = t_1;
	} else if (t <= 1.6e-266) {
		tmp = Math.exp((a * -b));
	} else if (t <= 1.22e+87) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	t_2 = math.exp((y * -t))
	tmp = 0
	if t <= -5e+25:
		tmp = t_2
	elif t <= -2.15e-191:
		tmp = t_1
	elif t <= 1.6e-266:
		tmp = math.exp((a * -b))
	elif t <= 1.22e+87:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	t_2 = exp(Float64(y * Float64(-t)))
	tmp = 0.0
	if (t <= -5e+25)
		tmp = t_2;
	elseif (t <= -2.15e-191)
		tmp = t_1;
	elseif (t <= 1.6e-266)
		tmp = exp(Float64(a * Float64(-b)));
	elseif (t <= 1.22e+87)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	t_2 = exp((y * -t));
	tmp = 0.0;
	if (t <= -5e+25)
		tmp = t_2;
	elseif (t <= -2.15e-191)
		tmp = t_1;
	elseif (t <= 1.6e-266)
		tmp = exp((a * -b));
	elseif (t <= 1.22e+87)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t, -5e+25], t$95$2, If[LessEqual[t, -2.15e-191], t$95$1, If[LessEqual[t, 1.6e-266], N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 1.22e+87], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.00000000000000024e25 or 1.2200000000000001e87 < t

   1. Initial program 97.3%

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

      1. add-exp-log 67.8%

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

      2. *-commutative 67.8%

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

      3. log-prod 43.5%

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

   4. Applied egg-rr 42.5%

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

   5. Taylor expanded in t around inf 54.1%

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

      1. associate-*r* 54.1%

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

      2. mul-1-neg 54.1%

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

   7. Simplified 54.1%

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

   if -5.00000000000000024e25 < t < -2.14999999999999992e-191 or 1.6e-266 < t < 1.2200000000000001e87

   1. Initial program 93.5%

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

   3. Taylor expanded in y around inf 67.0%

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

   4. Taylor expanded in t around 0 66.6%

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

   if -2.14999999999999992e-191 < t < 1.6e-266

   1. Initial program 93.6%

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

      1. add-exp-log 66.4%

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

      2. *-commutative 66.4%

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

      3. log-prod 39.8%

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

   4. Applied egg-rr 42.5%

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

   5. Taylor expanded in b around inf 50.9%

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

      1. associate-*r* 50.9%

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

      2. neg-mul-1 50.9%

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

   7. Simplified 50.9%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+25}:\\ \;\;\;\;e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-191}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-266}:\\ \;\;\;\;e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+87}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+26} \lor \neg \left(y \leq 1.75 \cdot 10^{-54}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9e+26) (not (<= y 1.75e-54)))
   (* x (exp (* y (- t))))
   (* x (exp (* (- a) (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e+26) || !(y <= 1.75e-54)) {
		tmp = x * exp((y * -t));
	} else {
		tmp = x * exp((-a * (z + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9d+26)) .or. (.not. (y <= 1.75d-54))) then
        tmp = x * exp((y * -t))
    else
        tmp = x * exp((-a * (z + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e+26) || !(y <= 1.75e-54)) {
		tmp = x * Math.exp((y * -t));
	} else {
		tmp = x * Math.exp((-a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9e+26) or not (y <= 1.75e-54):
		tmp = x * math.exp((y * -t))
	else:
		tmp = x * math.exp((-a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9e+26) || !(y <= 1.75e-54))
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	else
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9e+26) || ~((y <= 1.75e-54)))
		tmp = x * exp((y * -t));
	else
		tmp = x * exp((-a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9e+26], N[Not[LessEqual[y, 1.75e-54]], $MachinePrecision]], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999957e26 or 1.74999999999999991e-54 < y

   1. Initial program 99.2%

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

   3. Taylor expanded in t around inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. distribute-lft-neg-out 69.4%

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

      3. *-commutative 69.4%

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

   5. Simplified 69.4%

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

   if -8.99999999999999957e26 < y < 1.74999999999999991e-54

   1. Initial program 90.8%

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

   3. Taylor expanded in y around 0 78.9%

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

      1. sub-neg 78.9%

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

      2. log1p-define 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in z around 0 88.0%

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

      1. associate-*r* 88.0%

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

      2. associate-*r* 88.0%

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

      3. distribute-lft-out 88.0%

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

      4. mul-1-neg 88.0%

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

   8. Simplified 88.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+26} \lor \neg \left(y \leq 1.75 \cdot 10^{-54}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+77} \lor \neg \left(y \leq 1.15\right):\\ \;\;\;\;e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.5e+77) (not (<= y 1.15)))
   (exp (* y (- t)))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.5e+77) || !(y <= 1.15)) {
		tmp = exp((y * -t));
	} else {
		tmp = x * exp((a * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.5d+77)) .or. (.not. (y <= 1.15d0))) then
        tmp = exp((y * -t))
    else
        tmp = x * exp((a * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.5e+77) || !(y <= 1.15)) {
		tmp = Math.exp((y * -t));
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.5e+77) or not (y <= 1.15):
		tmp = math.exp((y * -t))
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.5e+77) || !(y <= 1.15))
		tmp = exp(Float64(y * Float64(-t)));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.5e+77) || ~((y <= 1.15)))
		tmp = exp((y * -t));
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.5e+77], N[Not[LessEqual[y, 1.15]], $MachinePrecision]], N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5000000000000001e77 or 1.1499999999999999 < y

   1. Initial program 99.1%

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

      1. add-exp-log 74.1%

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

      2. *-commutative 74.1%

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

      3. log-prod 45.5%

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

   4. Applied egg-rr 45.5%

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

   5. Taylor expanded in t around inf 48.9%

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

      1. associate-*r* 48.9%

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

      2. mul-1-neg 48.9%

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

   7. Simplified 48.9%

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

   if -3.5000000000000001e77 < y < 1.1499999999999999

   1. Initial program 91.9%

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

   3. Taylor expanded in b around inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. distribute-rgt-neg-out 75.2%

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

   5. Simplified 75.2%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+77} \lor \neg \left(y \leq 1.15\right):\\ \;\;\;\;e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-30} \lor \neg \left(y \leq 9.5 \cdot 10^{-56}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.45e-30) (not (<= y 9.5e-56)))
   (* x (exp (* y (- t))))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e-30) || !(y <= 9.5e-56)) {
		tmp = x * exp((y * -t));
	} else {
		tmp = x * exp((a * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.45d-30)) .or. (.not. (y <= 9.5d-56))) then
        tmp = x * exp((y * -t))
    else
        tmp = x * exp((a * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e-30) || !(y <= 9.5e-56)) {
		tmp = x * Math.exp((y * -t));
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.45e-30) or not (y <= 9.5e-56):
		tmp = x * math.exp((y * -t))
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.45e-30) || !(y <= 9.5e-56))
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.45e-30) || ~((y <= 9.5e-56)))
		tmp = x * exp((y * -t));
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.45e-30], N[Not[LessEqual[y, 9.5e-56]], $MachinePrecision]], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999995e-30 or 9.4999999999999991e-56 < y

   1. Initial program 99.3%

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

   3. Taylor expanded in t around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. distribute-lft-neg-out 68.5%

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

      3. *-commutative 68.5%

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

   5. Simplified 68.5%

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

   if -1.44999999999999995e-30 < y < 9.4999999999999991e-56

   1. Initial program 89.5%

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

   3. Taylor expanded in b around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. distribute-rgt-neg-out 80.4%

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

   5. Simplified 80.4%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-30} \lor \neg \left(y \leq 9.5 \cdot 10^{-56}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-9} \lor \neg \left(b \leq 6.8 \cdot 10^{-10}\right):\\ \;\;\;\;e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.05e-9) (not (<= b 6.8e-10)))
   (exp (* a (- b)))
   (* x (- 1.0 (* y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.05e-9) || !(b <= 6.8e-10)) {
		tmp = exp((a * -b));
	} else {
		tmp = x * (1.0 - (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 <= (-1.05d-9)) .or. (.not. (b <= 6.8d-10))) then
        tmp = exp((a * -b))
    else
        tmp = x * (1.0d0 - (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 <= -1.05e-9) || !(b <= 6.8e-10)) {
		tmp = Math.exp((a * -b));
	} else {
		tmp = x * (1.0 - (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.05e-9) or not (b <= 6.8e-10):
		tmp = math.exp((a * -b))
	else:
		tmp = x * (1.0 - (y * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.05e-9) || !(b <= 6.8e-10))
		tmp = exp(Float64(a * Float64(-b)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.05e-9) || ~((b <= 6.8e-10)))
		tmp = exp((a * -b));
	else
		tmp = x * (1.0 - (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.05e-9], N[Not[LessEqual[b, 6.8e-10]], $MachinePrecision]], N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.0500000000000001e-9 or 6.8000000000000003e-10 < b

   1. Initial program 98.6%

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

      1. add-exp-log 71.4%

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

      2. *-commutative 71.4%

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

      3. log-prod 41.7%

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

   4. Applied egg-rr 42.3%

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

   5. Taylor expanded in b around inf 46.6%

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

      1. associate-*r* 46.6%

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

      2. neg-mul-1 46.6%

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

   7. Simplified 46.6%

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

   if -1.0500000000000001e-9 < b < 6.8000000000000003e-10

   1. Initial program 90.9%

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

   3. Taylor expanded in t around inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. distribute-lft-neg-out 69.8%

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

      3. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in y around 0 37.3%

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

      1. associate-*r* 37.3%

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

      2. mul-1-neg 37.3%

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

   8. Simplified 37.3%

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

   9. Taylor expanded in x around 0 40.6%

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

       1. mul-1-neg 40.6%

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

       2. unsub-neg 40.6%

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

       3. *-commutative 40.6%

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

   11. Simplified 40.6%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-9} \lor \neg \left(b \leq 6.8 \cdot 10^{-10}\right):\\ \;\;\;\;e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.9% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{if}\;y \leq -6.7 \cdot 10^{+199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -12500000:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* x (- y)))))
   (if (<= y -6.7e+199)
     t_1
     (if (<= y -12500000.0)
       (* b (* x (- a)))
       (if (<= y -7e-119)
         t_1
         (if (<= y 5.5e-21) (* x (- 1.0 (* a b))) (* x (* y (- t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (x * -y);
	double tmp;
	if (y <= -6.7e+199) {
		tmp = t_1;
	} else if (y <= -12500000.0) {
		tmp = b * (x * -a);
	} else if (y <= -7e-119) {
		tmp = t_1;
	} else if (y <= 5.5e-21) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (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) :: t_1
    real(8) :: tmp
    t_1 = t * (x * -y)
    if (y <= (-6.7d+199)) then
        tmp = t_1
    else if (y <= (-12500000.0d0)) then
        tmp = b * (x * -a)
    else if (y <= (-7d-119)) then
        tmp = t_1
    else if (y <= 5.5d-21) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (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 t_1 = t * (x * -y);
	double tmp;
	if (y <= -6.7e+199) {
		tmp = t_1;
	} else if (y <= -12500000.0) {
		tmp = b * (x * -a);
	} else if (y <= -7e-119) {
		tmp = t_1;
	} else if (y <= 5.5e-21) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (x * -y)
	tmp = 0
	if y <= -6.7e+199:
		tmp = t_1
	elif y <= -12500000.0:
		tmp = b * (x * -a)
	elif y <= -7e-119:
		tmp = t_1
	elif y <= 5.5e-21:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(x * Float64(-y)))
	tmp = 0.0
	if (y <= -6.7e+199)
		tmp = t_1;
	elseif (y <= -12500000.0)
		tmp = Float64(b * Float64(x * Float64(-a)));
	elseif (y <= -7e-119)
		tmp = t_1;
	elseif (y <= 5.5e-21)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (x * -y);
	tmp = 0.0;
	if (y <= -6.7e+199)
		tmp = t_1;
	elseif (y <= -12500000.0)
		tmp = b * (x * -a);
	elseif (y <= -7e-119)
		tmp = t_1;
	elseif (y <= 5.5e-21)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.7e+199], t$95$1, If[LessEqual[y, -12500000.0], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-119], t$95$1, If[LessEqual[y, 5.5e-21], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.69999999999999987e199 or -1.25e7 < y < -7e-119

   1. Initial program 97.6%

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

   3. Taylor expanded in t around inf 65.4%

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

      1. mul-1-neg 65.4%

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

      2. distribute-lft-neg-out 65.4%

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

      3. *-commutative 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in y around 0 35.4%

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

      1. associate-*r* 35.4%

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

      2. mul-1-neg 35.4%

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

   8. Simplified 35.4%

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

   9. Taylor expanded in t around inf 37.5%

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

       1. +-commutative 37.5%

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

       2. mul-1-neg 37.5%

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

       3. unsub-neg 37.5%

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

   11. Simplified 37.5%

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

   12. Taylor expanded in t around inf 35.5%

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

       1. mul-1-neg 35.5%

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

       2. distribute-rgt-neg-in 35.5%

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

       3. distribute-rgt-neg-out 35.5%

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

   14. Simplified 35.5%

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

   if -6.69999999999999987e199 < y < -1.25e7

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 49.6%

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

      1. mul-1-neg 49.6%

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

      2. distribute-rgt-neg-out 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in a around 0 13.0%

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

      1. mul-1-neg 13.0%

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

      2. unsub-neg 13.0%

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

      3. *-commutative 13.0%

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

   8. Simplified 13.0%

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

   9. Taylor expanded in a around inf 24.5%

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

       1. *-commutative 24.5%

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

       2. associate-*r* 24.5%

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

       3. *-commutative 24.5%

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

       4. associate-*r* 26.7%

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

       5. associate-*r* 26.7%

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

       6. *-commutative 26.7%

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

       7. associate-*r* 26.7%

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

       8. neg-mul-1 26.7%

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

   11. Simplified 26.7%

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

   if -7e-119 < y < 5.49999999999999977e-21

   1. Initial program 88.6%

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

   3. Taylor expanded in b around inf 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-rgt-neg-out 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in a around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

   8. Simplified 51.4%

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

   if 5.49999999999999977e-21 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 66.3%

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

      1. mul-1-neg 66.3%

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

      2. distribute-lft-neg-out 66.3%

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

      3. *-commutative 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in y around 0 17.8%

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

      1. associate-*r* 17.8%

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

      2. mul-1-neg 17.8%

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

   8. Simplified 17.8%

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

   9. Taylor expanded in t around inf 17.6%

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

       1. +-commutative 17.6%

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

       2. mul-1-neg 17.6%

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

       3. unsub-neg 17.6%

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

   11. Simplified 17.6%

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

   12. Taylor expanded in t around inf 22.2%

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

       1. mul-1-neg 22.2%

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

       2. associate-*r* 25.7%

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

       3. distribute-rgt-neg-in 25.7%

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

       4. *-commutative 25.7%

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

       5. associate-*l* 30.1%

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

   14. Simplified 30.1%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+199}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -12500000:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 23.8% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* x (- a)))))
   (if (<= a -4.2e+61)
     t_1
     (if (<= a 1.2e-170)
       x
       (if (<= a 5.5e-18)
         (* t (* x (- y)))
         (if (<= a 3.5e+89) (* t (/ x t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (x * -a);
	double tmp;
	if (a <= -4.2e+61) {
		tmp = t_1;
	} else if (a <= 1.2e-170) {
		tmp = x;
	} else if (a <= 5.5e-18) {
		tmp = t * (x * -y);
	} else if (a <= 3.5e+89) {
		tmp = t * (x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (x * -a)
    if (a <= (-4.2d+61)) then
        tmp = t_1
    else if (a <= 1.2d-170) then
        tmp = x
    else if (a <= 5.5d-18) then
        tmp = t * (x * -y)
    else if (a <= 3.5d+89) then
        tmp = t * (x / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (x * -a);
	double tmp;
	if (a <= -4.2e+61) {
		tmp = t_1;
	} else if (a <= 1.2e-170) {
		tmp = x;
	} else if (a <= 5.5e-18) {
		tmp = t * (x * -y);
	} else if (a <= 3.5e+89) {
		tmp = t * (x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (x * -a)
	tmp = 0
	if a <= -4.2e+61:
		tmp = t_1
	elif a <= 1.2e-170:
		tmp = x
	elif a <= 5.5e-18:
		tmp = t * (x * -y)
	elif a <= 3.5e+89:
		tmp = t * (x / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(x * Float64(-a)))
	tmp = 0.0
	if (a <= -4.2e+61)
		tmp = t_1;
	elseif (a <= 1.2e-170)
		tmp = x;
	elseif (a <= 5.5e-18)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (a <= 3.5e+89)
		tmp = Float64(t * Float64(x / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (x * -a);
	tmp = 0.0;
	if (a <= -4.2e+61)
		tmp = t_1;
	elseif (a <= 1.2e-170)
		tmp = x;
	elseif (a <= 5.5e-18)
		tmp = t * (x * -y);
	elseif (a <= 3.5e+89)
		tmp = t * (x / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+61], t$95$1, If[LessEqual[a, 1.2e-170], x, If[LessEqual[a, 5.5e-18], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e+89], N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.2000000000000002e61 or 3.5000000000000001e89 < a

   1. Initial program 89.2%

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

   3. Taylor expanded in b around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. distribute-rgt-neg-out 66.6%

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

   5. Simplified 66.6%

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

   6. Taylor expanded in a around 0 29.8%

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

      1. mul-1-neg 29.8%

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

      2. unsub-neg 29.8%

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

      3. *-commutative 29.8%

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

   8. Simplified 29.8%

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

   9. Taylor expanded in a around inf 29.5%

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

       1. *-commutative 29.5%

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

       2. associate-*r* 30.1%

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

       3. *-commutative 30.1%

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

       4. associate-*r* 32.2%

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

       5. associate-*r* 32.2%

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

       6. *-commutative 32.2%

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

       7. associate-*r* 32.2%

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

       8. neg-mul-1 32.2%

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

   11. Simplified 32.2%

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

   if -4.2000000000000002e61 < a < 1.2e-170

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. distribute-rgt-neg-out 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in a around 0 32.4%

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

   if 1.2e-170 < a < 5.5e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 77.5%

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

      1. mul-1-neg 77.5%

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

      2. distribute-lft-neg-out 77.5%

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

      3. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in y around 0 43.4%

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

      1. associate-*r* 43.4%

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

      2. mul-1-neg 43.4%

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

   8. Simplified 43.4%

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

   9. Taylor expanded in t around inf 40.6%

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

       1. +-commutative 40.6%

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

       2. mul-1-neg 40.6%

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

       3. unsub-neg 40.6%

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

   11. Simplified 40.6%

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

   12. Taylor expanded in t around inf 34.6%

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

       1. mul-1-neg 34.6%

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

       2. distribute-rgt-neg-in 34.6%

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

       3. distribute-rgt-neg-out 34.6%

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

   14. Simplified 34.6%

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

   if 5.5e-18 < a < 3.5000000000000001e89

   1. Initial program 93.0%

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

   3. Taylor expanded in t around inf 43.0%

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

      1. mul-1-neg 43.0%

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

      2. distribute-lft-neg-out 43.0%

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

      3. *-commutative 43.0%

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

   5. Simplified 43.0%

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

   6. Taylor expanded in y around 0 10.8%

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

      1. associate-*r* 10.8%

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

      2. mul-1-neg 10.8%

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

   8. Simplified 10.8%

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

   9. Taylor expanded in t around inf 17.6%

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

       1. +-commutative 17.6%

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

       2. mul-1-neg 17.6%

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

       3. unsub-neg 17.6%

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

   11. Simplified 17.6%

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

   12. Taylor expanded in t around 0 24.7%

       \[\leadsto t \cdot \color{blue}{\frac{x}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+61}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 23.6% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* x (- a)))))
   (if (<= a -4.4e+61)
     t_1
     (if (<= a 1.08e-169) x (if (<= a 1.7e+148) (* x (* y (- t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (x * -a);
	double tmp;
	if (a <= -4.4e+61) {
		tmp = t_1;
	} else if (a <= 1.08e-169) {
		tmp = x;
	} else if (a <= 1.7e+148) {
		tmp = x * (y * -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (x * -a)
    if (a <= (-4.4d+61)) then
        tmp = t_1
    else if (a <= 1.08d-169) then
        tmp = x
    else if (a <= 1.7d+148) then
        tmp = x * (y * -t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (x * -a);
	double tmp;
	if (a <= -4.4e+61) {
		tmp = t_1;
	} else if (a <= 1.08e-169) {
		tmp = x;
	} else if (a <= 1.7e+148) {
		tmp = x * (y * -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (x * -a)
	tmp = 0
	if a <= -4.4e+61:
		tmp = t_1
	elif a <= 1.08e-169:
		tmp = x
	elif a <= 1.7e+148:
		tmp = x * (y * -t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(x * Float64(-a)))
	tmp = 0.0
	if (a <= -4.4e+61)
		tmp = t_1;
	elseif (a <= 1.08e-169)
		tmp = x;
	elseif (a <= 1.7e+148)
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (x * -a);
	tmp = 0.0;
	if (a <= -4.4e+61)
		tmp = t_1;
	elseif (a <= 1.08e-169)
		tmp = x;
	elseif (a <= 1.7e+148)
		tmp = x * (y * -t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.4e+61], t$95$1, If[LessEqual[a, 1.08e-169], x, If[LessEqual[a, 1.7e+148], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.4000000000000001e61 or 1.7000000000000001e148 < a

   1. Initial program 90.7%

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

   3. Taylor expanded in b around inf 73.6%

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

      1. mul-1-neg 73.6%

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

      2. distribute-rgt-neg-out 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in a around 0 32.7%

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

      1. mul-1-neg 32.7%

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

      2. unsub-neg 32.7%

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

      3. *-commutative 32.7%

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

   8. Simplified 32.7%

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

   9. Taylor expanded in a around inf 31.3%

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

       1. *-commutative 31.3%

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

       2. associate-*r* 32.6%

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

       3. *-commutative 32.6%

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

       4. associate-*r* 32.6%

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

       5. associate-*r* 32.6%

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

       6. *-commutative 32.6%

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

       7. associate-*r* 32.6%

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

       8. neg-mul-1 32.6%

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

   11. Simplified 32.6%

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

   if -4.4000000000000001e61 < a < 1.0799999999999999e-169

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. distribute-rgt-neg-out 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in a around 0 32.4%

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

   if 1.0799999999999999e-169 < a < 1.7000000000000001e148

   1. Initial program 93.8%

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

   3. Taylor expanded in t around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. distribute-lft-neg-out 61.5%

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

      3. *-commutative 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in y around 0 28.7%

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

      1. associate-*r* 28.7%

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

      2. mul-1-neg 28.7%

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

   8. Simplified 28.7%

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

   9. Taylor expanded in t around inf 31.0%

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

       1. +-commutative 31.0%

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

       2. mul-1-neg 31.0%

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

       3. unsub-neg 31.0%

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

   11. Simplified 31.0%

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

   12. Taylor expanded in t around inf 27.2%

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

       1. mul-1-neg 27.2%

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

       2. associate-*r* 27.2%

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

       3. distribute-rgt-neg-in 27.2%

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

       4. *-commutative 27.2%

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

       5. associate-*l* 33.3%

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

   14. Simplified 33.3%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+61}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 23.8% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.8e+61)
   (* x (* a (- b)))
   (if (<= a 8e-169)
     x
     (if (<= a 1.56e+147) (* x (* y (- t))) (* b (* x (- a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.8e+61) {
		tmp = x * (a * -b);
	} else if (a <= 8e-169) {
		tmp = x;
	} else if (a <= 1.56e+147) {
		tmp = x * (y * -t);
	} else {
		tmp = b * (x * -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 (a <= (-4.8d+61)) then
        tmp = x * (a * -b)
    else if (a <= 8d-169) then
        tmp = x
    else if (a <= 1.56d+147) then
        tmp = x * (y * -t)
    else
        tmp = b * (x * -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 (a <= -4.8e+61) {
		tmp = x * (a * -b);
	} else if (a <= 8e-169) {
		tmp = x;
	} else if (a <= 1.56e+147) {
		tmp = x * (y * -t);
	} else {
		tmp = b * (x * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.8e+61:
		tmp = x * (a * -b)
	elif a <= 8e-169:
		tmp = x
	elif a <= 1.56e+147:
		tmp = x * (y * -t)
	else:
		tmp = b * (x * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.8e+61)
		tmp = Float64(x * Float64(a * Float64(-b)));
	elseif (a <= 8e-169)
		tmp = x;
	elseif (a <= 1.56e+147)
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = Float64(b * Float64(x * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.8e+61)
		tmp = x * (a * -b);
	elseif (a <= 8e-169)
		tmp = x;
	elseif (a <= 1.56e+147)
		tmp = x * (y * -t);
	else
		tmp = b * (x * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.8e+61], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-169], x, If[LessEqual[a, 1.56e+147], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.7999999999999998e61

   1. Initial program 87.8%

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

   3. Taylor expanded in b around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-rgt-neg-out 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in a around 0 26.9%

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

      1. mul-1-neg 26.9%

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

      2. unsub-neg 26.9%

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

      3. *-commutative 26.9%

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

   8. Simplified 26.9%

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

   9. Taylor expanded in a around inf 26.8%

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

       1. *-commutative 26.8%

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

       2. associate-*r* 29.1%

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

       3. *-commutative 29.1%

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

       4. associate-*r* 29.1%

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

       5. associate-*r* 29.1%

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

       6. *-commutative 29.1%

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

       7. associate-*r* 29.1%

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

       8. neg-mul-1 29.1%

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

   11. Simplified 29.1%

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

   12. Taylor expanded in b around 0 26.8%

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

       1. associate-*r* 29.1%

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

       2. associate-*r* 29.1%

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

       3. *-commutative 29.1%

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

       4. associate-*r* 29.1%

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

       5. mul-1-neg 29.1%

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

   14. Simplified 29.1%

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

   if -4.7999999999999998e61 < a < 8.00000000000000016e-169

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. distribute-rgt-neg-out 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in a around 0 32.4%

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

   if 8.00000000000000016e-169 < a < 1.56e147

   1. Initial program 93.8%

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

   3. Taylor expanded in t around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. distribute-lft-neg-out 61.5%

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

      3. *-commutative 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in y around 0 28.7%

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

      1. associate-*r* 28.7%

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

      2. mul-1-neg 28.7%

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

   8. Simplified 28.7%

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

   9. Taylor expanded in t around inf 31.0%

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

       1. +-commutative 31.0%

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

       2. mul-1-neg 31.0%

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

       3. unsub-neg 31.0%

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

   11. Simplified 31.0%

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

   12. Taylor expanded in t around inf 27.2%

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

       1. mul-1-neg 27.2%

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

       2. associate-*r* 27.2%

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

       3. distribute-rgt-neg-in 27.2%

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

       4. *-commutative 27.2%

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

       5. associate-*l* 33.3%

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

   14. Simplified 33.3%

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

   if 1.56e147 < a

   1. Initial program 94.2%

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

   3. Taylor expanded in b around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-out 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in a around 0 39.5%

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

      1. mul-1-neg 39.5%

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

      2. unsub-neg 39.5%

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

      3. *-commutative 39.5%

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

   8. Simplified 39.5%

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

   9. Taylor expanded in a around inf 36.7%

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

       1. *-commutative 36.7%

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

       2. associate-*r* 36.7%

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

       3. *-commutative 36.7%

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

       4. associate-*r* 36.7%

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

       5. associate-*r* 36.7%

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

       6. *-commutative 36.7%

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

       7. associate-*r* 36.7%

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

       8. neg-mul-1 36.7%

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

   11. Simplified 36.7%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 24.2% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.2e+62)
   (* x (* a (- b)))
   (if (<= a 7.2e-169)
     x
     (if (<= a 8.5e+149) (* x (* y (- t))) (* a (* x (- b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.2e+62) {
		tmp = x * (a * -b);
	} else if (a <= 7.2e-169) {
		tmp = x;
	} else if (a <= 8.5e+149) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-3.2d+62)) then
        tmp = x * (a * -b)
    else if (a <= 7.2d-169) then
        tmp = x
    else if (a <= 8.5d+149) then
        tmp = x * (y * -t)
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.2e+62) {
		tmp = x * (a * -b);
	} else if (a <= 7.2e-169) {
		tmp = x;
	} else if (a <= 8.5e+149) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.2e+62:
		tmp = x * (a * -b)
	elif a <= 7.2e-169:
		tmp = x
	elif a <= 8.5e+149:
		tmp = x * (y * -t)
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.2e+62)
		tmp = Float64(x * Float64(a * Float64(-b)));
	elseif (a <= 7.2e-169)
		tmp = x;
	elseif (a <= 8.5e+149)
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.2e+62)
		tmp = x * (a * -b);
	elseif (a <= 7.2e-169)
		tmp = x;
	elseif (a <= 8.5e+149)
		tmp = x * (y * -t);
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.2e+62], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e-169], x, If[LessEqual[a, 8.5e+149], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.19999999999999984e62

   1. Initial program 87.8%

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

   3. Taylor expanded in b around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-rgt-neg-out 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in a around 0 26.9%

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

      1. mul-1-neg 26.9%

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

      2. unsub-neg 26.9%

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

      3. *-commutative 26.9%

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

   8. Simplified 26.9%

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

   9. Taylor expanded in a around inf 26.8%

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

       1. *-commutative 26.8%

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

       2. associate-*r* 29.1%

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

       3. *-commutative 29.1%

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

       4. associate-*r* 29.1%

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

       5. associate-*r* 29.1%

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

       6. *-commutative 29.1%

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

       7. associate-*r* 29.1%

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

       8. neg-mul-1 29.1%

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

   11. Simplified 29.1%

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

   12. Taylor expanded in b around 0 26.8%

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

       1. associate-*r* 29.1%

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

       2. associate-*r* 29.1%

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

       3. *-commutative 29.1%

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

       4. associate-*r* 29.1%

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

       5. mul-1-neg 29.1%

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

   14. Simplified 29.1%

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

   if -3.19999999999999984e62 < a < 7.20000000000000003e-169

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. distribute-rgt-neg-out 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in a around 0 32.4%

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

   if 7.20000000000000003e-169 < a < 8.49999999999999956e149

   1. Initial program 93.8%

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

   3. Taylor expanded in t around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. distribute-lft-neg-out 61.5%

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

      3. *-commutative 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in y around 0 28.7%

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

      1. associate-*r* 28.7%

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

      2. mul-1-neg 28.7%

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

   8. Simplified 28.7%

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

   9. Taylor expanded in t around inf 31.0%

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

       1. +-commutative 31.0%

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

       2. mul-1-neg 31.0%

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

       3. unsub-neg 31.0%

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

   11. Simplified 31.0%

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

   12. Taylor expanded in t around inf 27.2%

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

       1. mul-1-neg 27.2%

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

       2. associate-*r* 27.2%

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

       3. distribute-rgt-neg-in 27.2%

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

       4. *-commutative 27.2%

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

       5. associate-*l* 33.3%

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

   14. Simplified 33.3%

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

   if 8.49999999999999956e149 < a

   1. Initial program 94.2%

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

   3. Taylor expanded in b around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-out 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in a around 0 39.5%

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

      1. mul-1-neg 39.5%

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

      2. unsub-neg 39.5%

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

      3. *-commutative 39.5%

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

   8. Simplified 39.5%

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

   9. Taylor expanded in a around inf 36.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.2% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+35} \lor \neg \left(t \leq 1.12 \cdot 10^{+104}\right):\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.2e+35) (not (<= t 1.12e+104)))
   (* x (- 1.0 (* y t)))
   (* x (- 1.0 (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.2e+35) || !(t <= 1.12e+104)) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.2d+35)) .or. (.not. (t <= 1.12d+104))) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = x * (1.0d0 - (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.2e+35) || !(t <= 1.12e+104)) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.2e+35) or not (t <= 1.12e+104):
		tmp = x * (1.0 - (y * t))
	else:
		tmp = x * (1.0 - (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.2e+35) || !(t <= 1.12e+104))
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.2e+35) || ~((t <= 1.12e+104)))
		tmp = x * (1.0 - (y * t));
	else
		tmp = x * (1.0 - (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.2e+35], N[Not[LessEqual[t, 1.12e+104]], $MachinePrecision]], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.19999999999999983e35 or 1.12000000000000003e104 < t

   1. Initial program 97.2%

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

   3. Taylor expanded in t around inf 83.9%

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

      1. mul-1-neg 83.9%

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

      2. distribute-lft-neg-out 83.9%

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

      3. *-commutative 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in y around 0 30.1%

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

      1. associate-*r* 30.1%

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

      2. mul-1-neg 30.1%

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

   8. Simplified 30.1%

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

   9. Taylor expanded in x around 0 38.2%

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

       1. mul-1-neg 38.2%

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

       2. unsub-neg 38.2%

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

       3. *-commutative 38.2%

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

   11. Simplified 38.2%

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

   if -3.19999999999999983e35 < t < 1.12000000000000003e104

   1. Initial program 93.7%

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

   3. Taylor expanded in b around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. distribute-rgt-neg-out 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in a around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. unsub-neg 36.2%

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

   8. Simplified 36.2%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+35} \lor \neg \left(t \leq 1.12 \cdot 10^{+104}\right):\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.8% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.05 \cdot 10^{-21}:\\ \;\;\;\;b \cdot \left(\frac{x}{b} - x \cdot a\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.05e-21)
   (* b (- (/ x b) (* x a)))
   (if (<= a 1.55e+147) (* x (- 1.0 (* y t))) (- x (* a (* x b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.05e-21) {
		tmp = b * ((x / b) - (x * a));
	} else if (a <= 1.55e+147) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x - (a * (x * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-3.05d-21)) then
        tmp = b * ((x / b) - (x * a))
    else if (a <= 1.55d+147) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = x - (a * (x * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.05e-21) {
		tmp = b * ((x / b) - (x * a));
	} else if (a <= 1.55e+147) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x - (a * (x * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.05e-21:
		tmp = b * ((x / b) - (x * a))
	elif a <= 1.55e+147:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = x - (a * (x * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.05e-21)
		tmp = Float64(b * Float64(Float64(x / b) - Float64(x * a)));
	elseif (a <= 1.55e+147)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(x - Float64(a * Float64(x * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.05e-21)
		tmp = b * ((x / b) - (x * a));
	elseif (a <= 1.55e+147)
		tmp = x * (1.0 - (y * t));
	else
		tmp = x - (a * (x * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.05e-21], N[(b * N[(N[(x / b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+147], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.05000000000000007e-21

   1. Initial program 91.0%

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

   3. Taylor expanded in b around inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. distribute-rgt-neg-out 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in a around 0 26.3%

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

      1. mul-1-neg 26.3%

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

      2. unsub-neg 26.3%

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

      3. *-commutative 26.3%

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

   8. Simplified 26.3%

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

   9. Taylor expanded in b around inf 31.6%

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

       1. *-commutative 31.6%

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

   11. Simplified 31.6%

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

   if -3.05000000000000007e-21 < a < 1.55e147

   1. Initial program 96.6%

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

   3. Taylor expanded in t around inf 69.5%

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

      1. mul-1-neg 69.5%

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

      2. distribute-lft-neg-out 69.5%

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

      3. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in y around 0 35.7%

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

      1. associate-*r* 35.7%

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

      2. mul-1-neg 35.7%

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

   8. Simplified 35.7%

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

   9. Taylor expanded in x around 0 39.1%

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

       1. mul-1-neg 39.1%

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

       2. unsub-neg 39.1%

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

       3. *-commutative 39.1%

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

   11. Simplified 39.1%

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

   if 1.55e147 < a

   1. Initial program 94.2%

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

   3. Taylor expanded in b around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-out 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in a around 0 39.5%

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

      1. mul-1-neg 39.5%

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

      2. unsub-neg 39.5%

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

      3. *-commutative 39.5%

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

   8. Simplified 39.5%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.05 \cdot 10^{-21}:\\ \;\;\;\;b \cdot \left(\frac{x}{b} - x \cdot a\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.6% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+62} \lor \neg \left(a \leq 8.5 \cdot 10^{+88}\right):\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.4e+62) (not (<= a 8.5e+88)))
   (* b (* x (- a)))
   (* t (/ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.4e+62) || !(a <= 8.5e+88)) {
		tmp = b * (x * -a);
	} else {
		tmp = t * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.4d+62)) .or. (.not. (a <= 8.5d+88))) then
        tmp = b * (x * -a)
    else
        tmp = t * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.4e+62) || !(a <= 8.5e+88)) {
		tmp = b * (x * -a);
	} else {
		tmp = t * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.4e+62) or not (a <= 8.5e+88):
		tmp = b * (x * -a)
	else:
		tmp = t * (x / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.4e+62) || !(a <= 8.5e+88))
		tmp = Float64(b * Float64(x * Float64(-a)));
	else
		tmp = Float64(t * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.4e+62) || ~((a <= 8.5e+88)))
		tmp = b * (x * -a);
	else
		tmp = t * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.4e+62], N[Not[LessEqual[a, 8.5e+88]], $MachinePrecision]], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.40000000000000007e62 or 8.5000000000000005e88 < a

   1. Initial program 89.2%

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

   3. Taylor expanded in b around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. distribute-rgt-neg-out 66.6%

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

   5. Simplified 66.6%

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

   6. Taylor expanded in a around 0 29.8%

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

      1. mul-1-neg 29.8%

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

      2. unsub-neg 29.8%

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

      3. *-commutative 29.8%

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

   8. Simplified 29.8%

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

   9. Taylor expanded in a around inf 29.5%

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

       1. *-commutative 29.5%

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

       2. associate-*r* 30.1%

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

       3. *-commutative 30.1%

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

       4. associate-*r* 32.2%

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

       5. associate-*r* 32.2%

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

       6. *-commutative 32.2%

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

       7. associate-*r* 32.2%

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

       8. neg-mul-1 32.2%

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

   11. Simplified 32.2%

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

   if -1.40000000000000007e62 < a < 8.5000000000000005e88

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. distribute-lft-neg-out 69.7%

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

      3. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in y around 0 35.5%

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

      1. associate-*r* 35.5%

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

      2. mul-1-neg 35.5%

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

   8. Simplified 35.5%

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

   9. Taylor expanded in t around inf 31.5%

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

       1. +-commutative 31.5%

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

       2. mul-1-neg 31.5%

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

       3. unsub-neg 31.5%

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

   11. Simplified 31.5%

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

   12. Taylor expanded in t around 0 28.0%

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

4. Final simplification 29.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+62} \lor \neg \left(a \leq 8.5 \cdot 10^{+88}\right):\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 24.7% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -420000000000 \lor \neg \left(y \leq 3900\right):\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -420000000000.0) (not (<= y 3900.0))) (* a (* x b)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -420000000000.0) || !(y <= 3900.0)) {
		tmp = a * (x * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-420000000000.0d0)) .or. (.not. (y <= 3900.0d0))) then
        tmp = a * (x * b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -420000000000.0) || !(y <= 3900.0)) {
		tmp = a * (x * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -420000000000.0) or not (y <= 3900.0):
		tmp = a * (x * b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -420000000000.0) || !(y <= 3900.0))
		tmp = Float64(a * Float64(x * b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -420000000000.0) || ~((y <= 3900.0)))
		tmp = a * (x * b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -420000000000.0], N[Not[LessEqual[y, 3900.0]], $MachinePrecision]], N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e11 or 3900 < y

   1. Initial program 99.2%

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

   3. Taylor expanded in b around inf 32.8%

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

      1. mul-1-neg 32.8%

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

      2. distribute-rgt-neg-out 32.8%

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

   5. Simplified 32.8%

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

   6. Taylor expanded in a around 0 11.6%

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

      1. mul-1-neg 11.6%

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

      2. unsub-neg 11.6%

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

      3. *-commutative 11.6%

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

   8. Simplified 11.6%

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

   9. Taylor expanded in a around inf 20.0%

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

       1. *-commutative 20.0%

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

       2. associate-*r* 22.3%

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

       3. *-commutative 22.3%

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

       4. associate-*r* 21.9%

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

       5. associate-*r* 21.9%

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

       6. *-commutative 21.9%

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

       7. associate-*r* 21.9%

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

       8. neg-mul-1 21.9%

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

   11. Simplified 21.9%

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

       1. pow1 21.9%

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

       2. *-commutative 21.9%

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

       3. *-commutative 21.9%

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

       4. associate-*l* 22.3%

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

       5. add-sqr-sqrt 11.6%

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

       6. sqrt-unprod 29.9%

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

       7. sqr-neg 29.9%

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

       8. sqrt-unprod 7.7%

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

       9. add-sqr-sqrt 15.4%

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

   13. Applied egg-rr 15.4%

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

       1. unpow1 15.4%

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

       2. *-commutative 15.4%

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

       3. associate-*r* 16.8%

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

       4. *-commutative 16.8%

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

   15. Simplified 16.8%

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

   if -4.2e11 < y < 3900

   1. Initial program 91.1%

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

   3. Taylor expanded in b around inf 76.1%

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

      1. mul-1-neg 76.1%

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

      2. distribute-rgt-neg-out 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in a around 0 33.5%

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

4. Final simplification 25.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -420000000000 \lor \neg \left(y \leq 3900\right):\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 24.8% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ t \cdot \frac{x}{t} \end{array} \]

FPCore

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

C

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

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 = t * (x / t)
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	return Float64(t * Float64(x / t))
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.1%

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

3. Taylor expanded in t around inf 60.1%

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

   1. mul-1-neg 60.1%

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

   2. distribute-lft-neg-out 60.1%

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

   3. *-commutative 60.1%

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

5. Simplified 60.1%

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

6. Taylor expanded in y around 0 27.3%

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

   1. associate-*r* 27.3%

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

   2. mul-1-neg 27.3%

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

8. Simplified 27.3%

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

9. Taylor expanded in t around inf 26.5%

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

    1. +-commutative 26.5%

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

    2. mul-1-neg 26.5%

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

    3. unsub-neg 26.5%

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

11. Simplified 26.5%

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

12. Taylor expanded in t around 0 23.3%

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

13. Final simplification 23.3%

    \[\leadsto t \cdot \frac{x}{t} \]
14. Add Preprocessing

Alternative 20: 19.1% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.1%

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

3. Taylor expanded in b around inf 54.8%

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

   1. mul-1-neg 54.8%

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

   2. distribute-rgt-neg-out 54.8%

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

5. Simplified 54.8%

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

6. Taylor expanded in a around 0 19.0%

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

7. Final simplification 19.0%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(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))))))