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

Percentage Accurate: 96.5% → 99.5%

Time: 19.8s

Alternatives: 16

Speedup: 1.0×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% 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 95.5%

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

   1. fma-def 95.9%

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

   2. sub-neg 95.9%

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

   3. log1p-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

2. Final simplification 95.5%

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

Alternative 3: 86.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-44} \lor \neg \left(y \leq 1.3 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.8e-44) (not (<= y 1.3e+18)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (- b) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.8e-44) || !(y <= 1.3e+18)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * (-b - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.8d-44)) .or. (.not. (y <= 1.3d+18))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((a * (-b - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.8e-44) || !(y <= 1.3e+18)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * (-b - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.8e-44) or not (y <= 1.3e+18):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * (-b - z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.8e-44) || !(y <= 1.3e+18))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-b) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.8e-44) || ~((y <= 1.3e+18)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((a * (-b - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.8e-44], N[Not[LessEqual[y, 1.3e+18]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[((-b) - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.80000000000000033e-44 or 1.3e18 < y

   1. Initial program 97.7%

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

   2. Taylor expanded in y around inf 91.9%

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

   if -6.80000000000000033e-44 < y < 1.3e18

   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. Taylor expanded in y around 0 80.4%

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

      1. sub-neg 80.4%

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

      2. neg-mul-1 80.4%

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

      3. log1p-def 88.2%

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

      4. neg-mul-1 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in z around 0 88.2%

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

      1. associate-*r* 88.2%

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

      2. associate-*r* 88.2%

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

      3. distribute-lft-out 88.2%

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

      4. neg-mul-1 88.2%

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

   7. Simplified 88.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-44} \lor \neg \left(y \leq 1.3 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \end{array} \]

Alternative 4: 71.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{a \cdot \left(-b\right)}\\ t_2 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 305:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+154} \lor \neg \left(y \leq 1.7 \cdot 10^{+179}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* a (- b))))) (t_2 (* x (pow z y))))
   (if (<= y -1.5e+27)
     t_2
     (if (<= y 305.0)
       t_1
       (if (<= y 2.75e+104)
         t_2
         (if (<= y 8.5e+134)
           t_1
           (if (or (<= y 5.4e+154) (not (<= y 1.7e+179)))
             t_2
             (* (- y) (* x t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((a * -b));
	double t_2 = x * pow(z, y);
	double tmp;
	if (y <= -1.5e+27) {
		tmp = t_2;
	} else if (y <= 305.0) {
		tmp = t_1;
	} else if (y <= 2.75e+104) {
		tmp = t_2;
	} else if (y <= 8.5e+134) {
		tmp = t_1;
	} else if ((y <= 5.4e+154) || !(y <= 1.7e+179)) {
		tmp = t_2;
	} else {
		tmp = -y * (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * exp((a * -b))
    t_2 = x * (z ** y)
    if (y <= (-1.5d+27)) then
        tmp = t_2
    else if (y <= 305.0d0) then
        tmp = t_1
    else if (y <= 2.75d+104) then
        tmp = t_2
    else if (y <= 8.5d+134) then
        tmp = t_1
    else if ((y <= 5.4d+154) .or. (.not. (y <= 1.7d+179))) then
        tmp = t_2
    else
        tmp = -y * (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((a * -b));
	double t_2 = x * Math.pow(z, y);
	double tmp;
	if (y <= -1.5e+27) {
		tmp = t_2;
	} else if (y <= 305.0) {
		tmp = t_1;
	} else if (y <= 2.75e+104) {
		tmp = t_2;
	} else if (y <= 8.5e+134) {
		tmp = t_1;
	} else if ((y <= 5.4e+154) || !(y <= 1.7e+179)) {
		tmp = t_2;
	} else {
		tmp = -y * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((a * -b))
	t_2 = x * math.pow(z, y)
	tmp = 0
	if y <= -1.5e+27:
		tmp = t_2
	elif y <= 305.0:
		tmp = t_1
	elif y <= 2.75e+104:
		tmp = t_2
	elif y <= 8.5e+134:
		tmp = t_1
	elif (y <= 5.4e+154) or not (y <= 1.7e+179):
		tmp = t_2
	else:
		tmp = -y * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(a * Float64(-b))))
	t_2 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -1.5e+27)
		tmp = t_2;
	elseif (y <= 305.0)
		tmp = t_1;
	elseif (y <= 2.75e+104)
		tmp = t_2;
	elseif (y <= 8.5e+134)
		tmp = t_1;
	elseif ((y <= 5.4e+154) || !(y <= 1.7e+179))
		tmp = t_2;
	else
		tmp = Float64(Float64(-y) * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((a * -b));
	t_2 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -1.5e+27)
		tmp = t_2;
	elseif (y <= 305.0)
		tmp = t_1;
	elseif (y <= 2.75e+104)
		tmp = t_2;
	elseif (y <= 8.5e+134)
		tmp = t_1;
	elseif ((y <= 5.4e+154) || ~((y <= 1.7e+179)))
		tmp = t_2;
	else
		tmp = -y * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+27], t$95$2, If[LessEqual[y, 305.0], t$95$1, If[LessEqual[y, 2.75e+104], t$95$2, If[LessEqual[y, 8.5e+134], t$95$1, If[Or[LessEqual[y, 5.4e+154], N[Not[LessEqual[y, 1.7e+179]], $MachinePrecision]], t$95$2, N[((-y) * N[(x * t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.49999999999999988e27 or 305 < y < 2.75000000000000008e104 or 8.50000000000000024e134 < y < 5.40000000000000011e154 or 1.69999999999999998e179 < y

   1. Initial program 96.3%

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

   2. Taylor expanded in y around inf 94.5%

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

   3. Taylor expanded in t around 0 77.9%

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

   if -1.49999999999999988e27 < y < 305 or 2.75000000000000008e104 < y < 8.50000000000000024e134

   1. Initial program 94.6%

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

   2. Taylor expanded in b around inf 78.5%

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

      1. mul-1-neg 78.5%

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

      2. distribute-rgt-neg-out 78.5%

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

   4. Simplified 78.5%

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

   if 5.40000000000000011e154 < y < 1.69999999999999998e179

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 85.9%

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

      1. mul-1-neg 85.9%

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

      2. distribute-rgt-neg-in 85.9%

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

   4. Simplified 85.9%

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

   5. Taylor expanded in t around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. unsub-neg 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in t around inf 72.8%

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

      1. mul-1-neg 72.8%

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

      2. associate-*r* 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-lft-neg-in 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 305:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+104}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+134}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+154} \lor \neg \left(y \leq 1.7 \cdot 10^{+179}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 5: 74.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+65}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.5e+27)
   (* x (pow z y))
   (if (<= y 3e+65) (* x (exp (* a (- (- b) z)))) (* x (exp (* t (- y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.5e+27) {
		tmp = x * pow(z, y);
	} else if (y <= 3e+65) {
		tmp = x * exp((a * (-b - z)));
	} else {
		tmp = x * exp((t * -y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.5d+27)) then
        tmp = x * (z ** y)
    else if (y <= 3d+65) then
        tmp = x * exp((a * (-b - z)))
    else
        tmp = x * exp((t * -y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.5e+27) {
		tmp = x * Math.pow(z, y);
	} else if (y <= 3e+65) {
		tmp = x * Math.exp((a * (-b - z)));
	} else {
		tmp = x * Math.exp((t * -y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.5e+27:
		tmp = x * math.pow(z, y)
	elif y <= 3e+65:
		tmp = x * math.exp((a * (-b - z)))
	else:
		tmp = x * math.exp((t * -y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.5e+27)
		tmp = Float64(x * (z ^ y));
	elseif (y <= 3e+65)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-b) - z))));
	else
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.5e+27)
		tmp = x * (z ^ y);
	elseif (y <= 3e+65)
		tmp = x * exp((a * (-b - z)));
	else
		tmp = x * exp((t * -y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.5e+27], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+65], N[(x * N[Exp[N[(a * N[((-b) - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.49999999999999988e27

   1. Initial program 96.5%

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

   2. Taylor expanded in y around inf 96.5%

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

   3. Taylor expanded in t around 0 84.5%

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

   if -1.49999999999999988e27 < y < 3.0000000000000002e65

   1. Initial program 94.0%

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

   2. Taylor expanded in y around 0 76.8%

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

      1. sub-neg 76.8%

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

      2. neg-mul-1 76.8%

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

      3. log1p-def 84.7%

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

      4. neg-mul-1 84.7%

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

   4. Simplified 84.7%

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

   5. Taylor expanded in z around 0 84.7%

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

      1. associate-*r* 84.7%

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

      2. associate-*r* 84.7%

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

      3. distribute-lft-out 84.7%

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

      4. neg-mul-1 84.7%

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

   7. Simplified 84.7%

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

   if 3.0000000000000002e65 < y

   1. Initial program 98.2%

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

   2. Taylor expanded in t around inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. distribute-rgt-neg-in 73.5%

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

   4. Simplified 73.5%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+65}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \]

Alternative 6: 71.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+27}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 2750:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.1e+27)
   (* x (pow z y))
   (if (<= y 2750.0) (* x (exp (* a (- b)))) (* x (exp (* t (- y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.1e+27) {
		tmp = x * pow(z, y);
	} else if (y <= 2750.0) {
		tmp = x * exp((a * -b));
	} else {
		tmp = x * exp((t * -y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.1d+27)) then
        tmp = x * (z ** y)
    else if (y <= 2750.0d0) then
        tmp = x * exp((a * -b))
    else
        tmp = x * exp((t * -y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.1e+27) {
		tmp = x * Math.pow(z, y);
	} else if (y <= 2750.0) {
		tmp = x * Math.exp((a * -b));
	} else {
		tmp = x * Math.exp((t * -y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.1e+27:
		tmp = x * math.pow(z, y)
	elif y <= 2750.0:
		tmp = x * math.exp((a * -b))
	else:
		tmp = x * math.exp((t * -y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.1e+27)
		tmp = Float64(x * (z ^ y));
	elseif (y <= 2750.0)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	else
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.1e+27)
		tmp = x * (z ^ y);
	elseif (y <= 2750.0)
		tmp = x * exp((a * -b));
	else
		tmp = x * exp((t * -y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.1e+27], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2750.0], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.09999999999999995e27

   1. Initial program 96.5%

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

   2. Taylor expanded in y around inf 96.5%

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

   3. Taylor expanded in t around 0 84.5%

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

   if -2.09999999999999995e27 < y < 2750

   1. Initial program 94.3%

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

   2. Taylor expanded in b around inf 79.3%

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

      1. mul-1-neg 79.3%

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

      2. distribute-rgt-neg-out 79.3%

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

   4. Simplified 79.3%

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

   if 2750 < y

   1. Initial program 96.9%

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

   2. Taylor expanded in t around inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. distribute-rgt-neg-in 68.7%

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

   4. Simplified 68.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+27}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 2750:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \]

Alternative 7: 55.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -125000000:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -125000000.0) (- x (* x (* y t))) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -125000000.0) {
		tmp = x - (x * (y * t));
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-125000000.0d0)) then
        tmp = x - (x * (y * t))
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -125000000.0) {
		tmp = x - (x * (y * t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -125000000.0:
		tmp = x - (x * (y * t))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -125000000.0)
		tmp = Float64(x - Float64(x * Float64(y * t)));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -125000000.0)
		tmp = x - (x * (y * t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -125000000.0], N[(x - N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25e8

   1. Initial program 96.8%

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

   2. Taylor expanded in t around inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. distribute-rgt-neg-in 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in t around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. unsub-neg 41.2%

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

   7. Simplified 41.2%

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

      1. expm1-log1p-u 21.0%

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

      2. expm1-udef 21.0%

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

      3. *-commutative 21.0%

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

      4. associate-*l* 22.6%

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

   9. Applied egg-rr 22.6%

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

       1. expm1-def 22.6%

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

       2. expm1-log1p 42.7%

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

       3. *-commutative 42.7%

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

   11. Simplified 42.7%

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

   if -1.25e8 < t

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 69.0%

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

   3. Taylor expanded in t around 0 62.5%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -125000000:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 8: 33.6% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+172}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.2e+172)
   (* t (* x (- y)))
   (if (<= y 5.6e+89) (* x (- 1.0 (* a (+ z b)))) (* (- y) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.2e+172) {
		tmp = t * (x * -y);
	} else if (y <= 5.6e+89) {
		tmp = x * (1.0 - (a * (z + b)));
	} else {
		tmp = -y * (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9.2d+172)) then
        tmp = t * (x * -y)
    else if (y <= 5.6d+89) then
        tmp = x * (1.0d0 - (a * (z + b)))
    else
        tmp = -y * (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.2e+172) {
		tmp = t * (x * -y);
	} else if (y <= 5.6e+89) {
		tmp = x * (1.0 - (a * (z + b)));
	} else {
		tmp = -y * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.2e+172:
		tmp = t * (x * -y)
	elif y <= 5.6e+89:
		tmp = x * (1.0 - (a * (z + b)))
	else:
		tmp = -y * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.2e+172)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 5.6e+89)
		tmp = Float64(x * Float64(1.0 - Float64(a * Float64(z + b))));
	else
		tmp = Float64(Float64(-y) * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9.2e+172)
		tmp = t * (x * -y);
	elseif (y <= 5.6e+89)
		tmp = x * (1.0 - (a * (z + b)));
	else
		tmp = -y * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.2e+172], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+89], N[(x * N[(1.0 - N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-y) * N[(x * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.2000000000000003e172

   1. Initial program 96.8%

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

   2. Taylor expanded in t around inf 77.9%

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

      1. mul-1-neg 77.9%

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

      2. distribute-rgt-neg-in 77.9%

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

   4. Simplified 77.9%

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

   5. Taylor expanded in t around 0 40.3%

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

      1. mul-1-neg 40.3%

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

      2. unsub-neg 40.3%

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

   7. Simplified 40.3%

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

   8. Taylor expanded in t around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. associate-*r* 28.2%

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

      3. *-commutative 28.2%

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

      4. distribute-lft-neg-in 28.2%

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

   10. Simplified 28.2%

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

   11. Taylor expanded in x around 0 40.3%

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

       1. mul-1-neg 40.3%

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

       2. distribute-rgt-neg-in 40.3%

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

       3. *-commutative 40.3%

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

       4. distribute-rgt-neg-in 40.3%

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

   13. Simplified 40.3%

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

   if -9.2000000000000003e172 < y < 5.5999999999999996e89

   1. Initial program 94.5%

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

   2. Taylor expanded in y around 0 69.7%

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

      1. sub-neg 69.7%

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

      2. neg-mul-1 69.7%

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

      3. log1p-def 76.3%

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

      4. neg-mul-1 76.3%

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

   4. Simplified 76.3%

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

   5. Taylor expanded in z around 0 76.3%

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

      1. associate-*r* 76.3%

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

      2. associate-*r* 76.3%

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

      3. distribute-lft-out 76.3%

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

      4. neg-mul-1 76.3%

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

   7. Simplified 76.3%

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

   8. Taylor expanded in a around 0 37.3%

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

      1. mul-1-neg 37.3%

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

      2. unsub-neg 37.3%

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

   10. Simplified 37.3%

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

   if 5.5999999999999996e89 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 73.3%

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

      1. mul-1-neg 73.3%

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

      2. distribute-rgt-neg-in 73.3%

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

   4. Simplified 73.3%

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

   5. Taylor expanded in t around 0 31.3%

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

      1. mul-1-neg 31.3%

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

      2. unsub-neg 31.3%

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

   7. Simplified 31.3%

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

   8. Taylor expanded in t around inf 33.2%

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

      1. mul-1-neg 33.2%

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

      2. associate-*r* 38.8%

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

      3. *-commutative 38.8%

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

      4. distribute-lft-neg-in 38.8%

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

   10. Simplified 38.8%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+172}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 9: 27.5% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{if}\;y \leq -9500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+108}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* x (- y)))))
   (if (<= y -9500.0)
     t_1
     (if (<= y 2.3e-81) x (if (<= y 1e+108) (* x (* a (- b))) t_1)))))

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 <= -9500.0) {
		tmp = t_1;
	} else if (y <= 2.3e-81) {
		tmp = x;
	} else if (y <= 1e+108) {
		tmp = x * (a * -b);
	} 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 = t * (x * -y)
    if (y <= (-9500.0d0)) then
        tmp = t_1
    else if (y <= 2.3d-81) then
        tmp = x
    else if (y <= 1d+108) then
        tmp = x * (a * -b)
    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 = t * (x * -y);
	double tmp;
	if (y <= -9500.0) {
		tmp = t_1;
	} else if (y <= 2.3e-81) {
		tmp = x;
	} else if (y <= 1e+108) {
		tmp = x * (a * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (x * -y)
	tmp = 0
	if y <= -9500.0:
		tmp = t_1
	elif y <= 2.3e-81:
		tmp = x
	elif y <= 1e+108:
		tmp = x * (a * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(x * Float64(-y)))
	tmp = 0.0
	if (y <= -9500.0)
		tmp = t_1;
	elseif (y <= 2.3e-81)
		tmp = x;
	elseif (y <= 1e+108)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = t_1;
	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 <= -9500.0)
		tmp = t_1;
	elseif (y <= 2.3e-81)
		tmp = x;
	elseif (y <= 1e+108)
		tmp = x * (a * -b);
	else
		tmp = t_1;
	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, -9500.0], t$95$1, If[LessEqual[y, 2.3e-81], x, If[LessEqual[y, 1e+108], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9500 or 1e108 < y

   1. Initial program 97.1%

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

   2. Taylor expanded in t around inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. distribute-rgt-neg-in 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in t around 0 29.3%

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

      1. mul-1-neg 29.3%

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

      2. unsub-neg 29.3%

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

   7. Simplified 29.3%

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

   8. Taylor expanded in t around inf 30.9%

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

      1. mul-1-neg 30.9%

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

      2. associate-*r* 30.0%

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

      3. *-commutative 30.0%

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

      4. distribute-lft-neg-in 30.0%

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

   10. Simplified 30.0%

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

   11. Taylor expanded in x around 0 30.9%

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

       1. mul-1-neg 30.9%

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

       2. distribute-rgt-neg-in 30.9%

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

       3. *-commutative 30.9%

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

       4. distribute-rgt-neg-in 30.9%

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

   13. Simplified 30.9%

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

   if -9500 < y < 2.29999999999999991e-81

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf 51.7%

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

   3. Taylor expanded in y around 0 32.6%

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

   if 2.29999999999999991e-81 < y < 1e108

   1. Initial program 97.7%

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

   2. Taylor expanded in b around inf 54.8%

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

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

   4. Simplified 54.8%

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

   5. Taylor expanded in a around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. unsub-neg 36.2%

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

   7. Simplified 36.2%

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

   8. Taylor expanded in a around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. *-commutative 40.3%

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

      3. distribute-rgt-neg-in 40.3%

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

   10. Simplified 40.3%

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

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9500:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+108}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 10: 28.1% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9500:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9500.0)
   (* t (* x (- y)))
   (if (<= y 4e-87)
     x
     (if (<= y 6.2e+107) (* x (* a (- b))) (* x (* t (- y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9500.0) {
		tmp = t * (x * -y);
	} else if (y <= 4e-87) {
		tmp = x;
	} else if (y <= 6.2e+107) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (t * -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9500.0d0)) then
        tmp = t * (x * -y)
    else if (y <= 4d-87) then
        tmp = x
    else if (y <= 6.2d+107) then
        tmp = x * (a * -b)
    else
        tmp = x * (t * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9500.0) {
		tmp = t * (x * -y);
	} else if (y <= 4e-87) {
		tmp = x;
	} else if (y <= 6.2e+107) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (t * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9500.0:
		tmp = t * (x * -y)
	elif y <= 4e-87:
		tmp = x
	elif y <= 6.2e+107:
		tmp = x * (a * -b)
	else:
		tmp = x * (t * -y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9500.0)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 4e-87)
		tmp = x;
	elseif (y <= 6.2e+107)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = Float64(x * Float64(t * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9500.0)
		tmp = t * (x * -y);
	elseif (y <= 4e-87)
		tmp = x;
	elseif (y <= 6.2e+107)
		tmp = x * (a * -b);
	else
		tmp = x * (t * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9500.0], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-87], x, If[LessEqual[y, 6.2e+107], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-y)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9500

   1. Initial program 96.7%

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

   2. Taylor expanded in t around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-rgt-neg-in 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in t around 0 27.2%

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

      1. mul-1-neg 27.2%

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

      2. unsub-neg 27.2%

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

   7. Simplified 27.2%

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

   8. Taylor expanded in t around inf 28.3%

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

      1. mul-1-neg 28.3%

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

      2. associate-*r* 22.1%

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

      3. *-commutative 22.1%

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

      4. distribute-lft-neg-in 22.1%

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

   10. Simplified 22.1%

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

   11. Taylor expanded in x around 0 28.3%

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

       1. mul-1-neg 28.3%

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

       2. distribute-rgt-neg-in 28.3%

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

       3. *-commutative 28.3%

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

       4. distribute-rgt-neg-in 28.3%

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

   13. Simplified 28.3%

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

   if -9500 < y < 4.00000000000000007e-87

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf 51.7%

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

   3. Taylor expanded in y around 0 32.6%

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

   if 4.00000000000000007e-87 < y < 6.20000000000000052e107

   1. Initial program 97.7%

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

   2. Taylor expanded in b around inf 54.8%

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

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

   4. Simplified 54.8%

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

   5. Taylor expanded in a around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. unsub-neg 36.2%

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

   7. Simplified 36.2%

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

   8. Taylor expanded in a around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. *-commutative 40.3%

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

      3. distribute-rgt-neg-in 40.3%

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

   10. Simplified 40.3%

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

   if 6.20000000000000052e107 < y

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. distribute-rgt-neg-in 77.4%

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

   4. Simplified 77.4%

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

   5. Taylor expanded in t around 0 32.2%

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

      1. mul-1-neg 32.2%

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

      2. unsub-neg 32.2%

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

   7. Simplified 32.2%

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

   8. Taylor expanded in t around inf 34.4%

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

      1. mul-1-neg 34.4%

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

      2. *-commutative 34.4%

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

      3. associate-*r* 36.7%

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

      4. distribute-lft-neg-in 36.7%

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

      5. *-commutative 36.7%

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

   10. Simplified 36.7%

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

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9500:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 11: 28.9% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9600:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9600.0)
   (* t (* x (- y)))
   (if (<= y 1.45e-81)
     x
     (if (<= y 1.1e+108) (* x (* a (- b))) (* (- y) (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9600.0) {
		tmp = t * (x * -y);
	} else if (y <= 1.45e-81) {
		tmp = x;
	} else if (y <= 1.1e+108) {
		tmp = x * (a * -b);
	} else {
		tmp = -y * (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9600.0d0)) then
        tmp = t * (x * -y)
    else if (y <= 1.45d-81) then
        tmp = x
    else if (y <= 1.1d+108) then
        tmp = x * (a * -b)
    else
        tmp = -y * (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9600.0) {
		tmp = t * (x * -y);
	} else if (y <= 1.45e-81) {
		tmp = x;
	} else if (y <= 1.1e+108) {
		tmp = x * (a * -b);
	} else {
		tmp = -y * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9600.0:
		tmp = t * (x * -y)
	elif y <= 1.45e-81:
		tmp = x
	elif y <= 1.1e+108:
		tmp = x * (a * -b)
	else:
		tmp = -y * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9600.0)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 1.45e-81)
		tmp = x;
	elseif (y <= 1.1e+108)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = Float64(Float64(-y) * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9600.0)
		tmp = t * (x * -y);
	elseif (y <= 1.45e-81)
		tmp = x;
	elseif (y <= 1.1e+108)
		tmp = x * (a * -b);
	else
		tmp = -y * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9600.0], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-81], x, If[LessEqual[y, 1.1e+108], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[((-y) * N[(x * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9600

   1. Initial program 96.7%

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

   2. Taylor expanded in t around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-rgt-neg-in 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in t around 0 27.2%

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

      1. mul-1-neg 27.2%

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

      2. unsub-neg 27.2%

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

   7. Simplified 27.2%

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

   8. Taylor expanded in t around inf 28.3%

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

      1. mul-1-neg 28.3%

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

      2. associate-*r* 22.1%

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

      3. *-commutative 22.1%

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

      4. distribute-lft-neg-in 22.1%

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

   10. Simplified 22.1%

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

   11. Taylor expanded in x around 0 28.3%

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

       1. mul-1-neg 28.3%

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

       2. distribute-rgt-neg-in 28.3%

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

       3. *-commutative 28.3%

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

       4. distribute-rgt-neg-in 28.3%

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

   13. Simplified 28.3%

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

   if -9600 < y < 1.44999999999999994e-81

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf 51.7%

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

   3. Taylor expanded in y around 0 32.6%

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

   if 1.44999999999999994e-81 < y < 1.1000000000000001e108

   1. Initial program 97.7%

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

   2. Taylor expanded in b around inf 54.8%

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

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

   4. Simplified 54.8%

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

   5. Taylor expanded in a around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. unsub-neg 36.2%

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

   7. Simplified 36.2%

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

   8. Taylor expanded in a around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. *-commutative 40.3%

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

      3. distribute-rgt-neg-in 40.3%

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

   10. Simplified 40.3%

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

   if 1.1000000000000001e108 < y

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. distribute-rgt-neg-in 77.4%

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

   4. Simplified 77.4%

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

   5. Taylor expanded in t around 0 32.2%

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

      1. mul-1-neg 32.2%

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

      2. unsub-neg 32.2%

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

   7. Simplified 32.2%

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

   8. Taylor expanded in t around inf 34.4%

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

      1. mul-1-neg 34.4%

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

      2. associate-*r* 41.0%

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

      3. *-commutative 41.0%

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

      4. distribute-lft-neg-in 41.0%

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

   10. Simplified 41.0%

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

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9600:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 12: 33.3% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.4e+171)
   (* t (* x (- y)))
   (if (<= y 2.3e+86) (* x (- 1.0 (* a b))) (* (- y) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.4e+171) {
		tmp = t * (x * -y);
	} else if (y <= 2.3e+86) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = -y * (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.4d+171)) then
        tmp = t * (x * -y)
    else if (y <= 2.3d+86) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = -y * (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.4e+171) {
		tmp = t * (x * -y);
	} else if (y <= 2.3e+86) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = -y * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.4e+171:
		tmp = t * (x * -y)
	elif y <= 2.3e+86:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = -y * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.4e+171)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 2.3e+86)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(Float64(-y) * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.4e+171)
		tmp = t * (x * -y);
	elseif (y <= 2.3e+86)
		tmp = x * (1.0 - (a * b));
	else
		tmp = -y * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.4e+171], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+86], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-y) * N[(x * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3999999999999996e171

   1. Initial program 96.8%

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

   2. Taylor expanded in t around inf 77.9%

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

      1. mul-1-neg 77.9%

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

      2. distribute-rgt-neg-in 77.9%

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

   4. Simplified 77.9%

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

   5. Taylor expanded in t around 0 40.3%

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

      1. mul-1-neg 40.3%

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

      2. unsub-neg 40.3%

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

   7. Simplified 40.3%

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

   8. Taylor expanded in t around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. associate-*r* 28.2%

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

      3. *-commutative 28.2%

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

      4. distribute-lft-neg-in 28.2%

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

   10. Simplified 28.2%

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

   11. Taylor expanded in x around 0 40.3%

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

       1. mul-1-neg 40.3%

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

       2. distribute-rgt-neg-in 40.3%

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

       3. *-commutative 40.3%

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

       4. distribute-rgt-neg-in 40.3%

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

   13. Simplified 40.3%

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

   if -5.3999999999999996e171 < y < 2.2999999999999999e86

   1. Initial program 94.5%

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

   2. Taylor expanded in b around inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-rgt-neg-out 69.2%

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

   4. Simplified 69.2%

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

   5. Taylor expanded in a around 0 36.8%

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

      1. mul-1-neg 36.8%

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

      2. unsub-neg 36.8%

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

   7. Simplified 36.8%

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

   if 2.2999999999999999e86 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 73.3%

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

      1. mul-1-neg 73.3%

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

      2. distribute-rgt-neg-in 73.3%

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

   4. Simplified 73.3%

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

   5. Taylor expanded in t around 0 31.3%

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

      1. mul-1-neg 31.3%

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

      2. unsub-neg 31.3%

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

   7. Simplified 31.3%

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

   8. Taylor expanded in t around inf 33.2%

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

      1. mul-1-neg 33.2%

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

      2. associate-*r* 38.8%

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

      3. *-commutative 38.8%

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

      4. distribute-lft-neg-in 38.8%

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

   10. Simplified 38.8%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 13: 26.1% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9600 \lor \neg \left(y \leq 4.1 \cdot 10^{-84}\right):\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9600.0) (not (<= y 4.1e-84))) (* t (* x (- y))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9600.0) || !(y <= 4.1e-84)) {
		tmp = t * (x * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9600.0d0)) .or. (.not. (y <= 4.1d-84))) then
        tmp = t * (x * -y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9600.0) || !(y <= 4.1e-84)) {
		tmp = t * (x * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9600.0) or not (y <= 4.1e-84):
		tmp = t * (x * -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9600.0) || !(y <= 4.1e-84))
		tmp = Float64(t * Float64(x * Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9600.0) || ~((y <= 4.1e-84)))
		tmp = t * (x * -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9600.0], N[Not[LessEqual[y, 4.1e-84]], $MachinePrecision]], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9600 or 4.10000000000000005e-84 < y

   1. Initial program 97.3%

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

   2. Taylor expanded in t around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. distribute-rgt-neg-in 63.2%

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

   4. Simplified 63.2%

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

   5. Taylor expanded in t around 0 26.5%

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

      1. mul-1-neg 26.5%

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

      2. unsub-neg 26.5%

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

   7. Simplified 26.5%

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

   8. Taylor expanded in t around inf 26.8%

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

      1. mul-1-neg 26.8%

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

      2. associate-*r* 25.5%

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

      3. *-commutative 25.5%

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

      4. distribute-lft-neg-in 25.5%

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

   10. Simplified 25.5%

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

   11. Taylor expanded in x around 0 26.8%

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

       1. mul-1-neg 26.8%

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

       2. distribute-rgt-neg-in 26.8%

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

       3. *-commutative 26.8%

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

       4. distribute-rgt-neg-in 26.8%

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

   13. Simplified 26.8%

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

   if -9600 < y < 4.10000000000000005e-84

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf 51.7%

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

   3. Taylor expanded in y around 0 32.6%

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

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9600 \lor \neg \left(y \leq 4.1 \cdot 10^{-84}\right):\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 22.0% accurate, 34.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-123}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.1e-123) (* (- a) (* x z)) (if (<= a 8.5e+103) x (* x (* y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.1e-123) {
		tmp = -a * (x * z);
	} else if (a <= 8.5e+103) {
		tmp = x;
	} 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) :: tmp
    if (a <= (-1.1d-123)) then
        tmp = -a * (x * z)
    else if (a <= 8.5d+103) then
        tmp = x
    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 tmp;
	if (a <= -1.1e-123) {
		tmp = -a * (x * z);
	} else if (a <= 8.5e+103) {
		tmp = x;
	} else {
		tmp = x * (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.1e-123:
		tmp = -a * (x * z)
	elif a <= 8.5e+103:
		tmp = x
	else:
		tmp = x * (y * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.1e-123)
		tmp = Float64(Float64(-a) * Float64(x * z));
	elseif (a <= 8.5e+103)
		tmp = x;
	else
		tmp = Float64(x * Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.1e-123)
		tmp = -a * (x * z);
	elseif (a <= 8.5e+103)
		tmp = x;
	else
		tmp = x * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.1e-123], N[((-a) * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+103], x, N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.10000000000000003e-123

   1. Initial program 91.6%

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

   2. Taylor expanded in y around 0 59.0%

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

      1. sub-neg 59.0%

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

      2. neg-mul-1 59.0%

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

      3. log1p-def 69.4%

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

      4. neg-mul-1 69.4%

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

   4. Simplified 69.4%

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

   5. Taylor expanded in z around 0 69.4%

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

      1. associate-*r* 69.4%

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

      2. associate-*r* 69.4%

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

      3. distribute-lft-out 69.4%

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

      4. neg-mul-1 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in a around 0 21.9%

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

      1. mul-1-neg 21.9%

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

      2. unsub-neg 21.9%

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

   10. Simplified 21.9%

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

   11. Taylor expanded in z around inf 19.0%

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

       1. mul-1-neg 19.0%

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

       2. distribute-rgt-neg-in 19.0%

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

       3. *-commutative 19.0%

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

   13. Simplified 19.0%

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

   if -1.10000000000000003e-123 < a < 8.4999999999999992e103

   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. Taylor expanded in y around inf 89.5%

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

   3. Taylor expanded in y around 0 30.0%

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

   if 8.4999999999999992e103 < a

   1. Initial program 93.1%

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

   2. Taylor expanded in t around inf 24.4%

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

      1. mul-1-neg 24.4%

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

      2. distribute-rgt-neg-in 24.4%

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

   4. Simplified 24.4%

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

   5. Taylor expanded in t around 0 10.6%

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

      1. mul-1-neg 10.6%

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

      2. unsub-neg 10.6%

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

   7. Simplified 10.6%

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

   8. Taylor expanded in t around inf 25.1%

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

      1. mul-1-neg 25.1%

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

      2. associate-*r* 25.1%

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

      3. *-commutative 25.1%

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

      4. distribute-lft-neg-in 25.1%

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

   10. Simplified 25.1%

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

       1. expm1-log1p-u 19.9%

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

       2. expm1-udef 41.2%

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

       3. add-sqr-sqrt 21.9%

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

       4. sqrt-unprod 41.3%

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

       5. sqr-neg 41.3%

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

       6. sqrt-unprod 28.9%

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

       7. add-sqr-sqrt 38.8%

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

       8. associate-*l* 38.8%

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

   12. Applied egg-rr 38.8%

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

       1. expm1-def 19.7%

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

       2. expm1-log1p 20.0%

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

   14. Simplified 20.0%

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

4. Final simplification 24.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-123}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 15: 23.1% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 1.55e+16) x (* a (* x b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.55e+16) {
		tmp = x;
	} else {
		tmp = a * (x * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.55d+16) then
        tmp = x
    else
        tmp = a * (x * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.55e+16) {
		tmp = x;
	} else {
		tmp = a * (x * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.55e+16:
		tmp = x
	else:
		tmp = a * (x * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.55e+16)
		tmp = x;
	else
		tmp = Float64(a * Float64(x * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.55e+16)
		tmp = x;
	else
		tmp = a * (x * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.55e+16], x, N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.55e16

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf 65.3%

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

   3. Taylor expanded in y around 0 21.3%

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

   if 1.55e16 < y

   1. Initial program 98.4%

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

   2. Taylor expanded in b around inf 33.7%

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

      1. mul-1-neg 33.7%

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

      2. distribute-rgt-neg-out 33.7%

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

   4. Simplified 33.7%

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

   5. Taylor expanded in a around 0 11.8%

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

      1. mul-1-neg 11.8%

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

      2. unsub-neg 11.8%

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

   7. Simplified 11.8%

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

   8. Taylor expanded in a around inf 24.3%

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

      1. mul-1-neg 24.3%

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

      2. *-commutative 24.3%

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

      3. distribute-rgt-neg-in 24.3%

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

   10. Simplified 24.3%

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

       1. associate-*r* 23.4%

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

       2. *-commutative 23.4%

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

       3. add-sqr-sqrt 9.0%

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

       4. sqrt-unprod 32.0%

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

       5. sqr-neg 32.0%

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

       6. sqrt-unprod 15.6%

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

       7. add-sqr-sqrt 21.3%

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

       8. expm1-log1p-u 21.0%

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

       9. *-commutative 21.0%

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

       10. expm1-udef 34.7%

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

       11. *-commutative 34.7%

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

   12. Applied egg-rr 34.7%

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

       1. expm1-def 21.0%

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

       2. expm1-log1p 21.3%

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

   14. Simplified 21.3%

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

4. Final simplification 21.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \]

Alternative 16: 19.4% 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 95.5%

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

2. Taylor expanded in y around inf 71.8%

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

3. Taylor expanded in y around 0 17.2%

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

4. Final simplification 17.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023310 
(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))))))