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

Percentage Accurate: 96.5% → 99.6%

Time: 18.0s

Alternatives: 17

Speedup: 0.8×

• 42.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

   1. fma-define 94.6%

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

   2. sub-neg 94.6%

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

   3. log1p-define 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 96.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+194}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.2e+194)
   (* x (exp (* a (- (- z) b))))
   (* 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) {
	double tmp;
	if (a <= -6.2e+194) {
		tmp = x * exp((a * (-z - b)));
	} else {
		tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-6.2d+194)) then
        tmp = x * exp((a * (-z - b)))
    else
        tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.2e+194) {
		tmp = x * Math.exp((a * (-z - b)));
	} else {
		tmp = x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.2e+194:
		tmp = x * math.exp((a * (-z - b)))
	else:
		tmp = x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.2e+194)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	else
		tmp = Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6.2e+194)
		tmp = x * exp((a * (-z - b)));
	else
		tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.2e+194], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 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. Split input into 2 regimes

2. if a < -6.1999999999999999e194

   1. Initial program 76.5%

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

   3. Taylor expanded in y around 0 70.3%

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

      1. sub-neg 70.3%

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

      2. log1p-define 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in z around 0 93.6%

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

      1. +-commutative 93.6%

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

      2. associate-*r* 93.6%

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

      3. associate-*r* 93.6%

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

      4. distribute-lft-out 93.6%

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

      5. mul-1-neg 93.6%

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

   8. Simplified 93.6%

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

   if -6.1999999999999999e194 < a

   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. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+194}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -35000000 \lor \neg \left(y \leq 5.4 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot {\left(\frac{z}{e^{t}}\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -35000000.0) (not (<= y 5.4e-7)))
   (* x (pow (/ z (exp t)) y))
   (* x (exp (* a (- (- z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -35000000.0) || !(y <= 5.4e-7)) {
		tmp = x * pow((z / exp(t)), y);
	} else {
		tmp = x * exp((a * (-z - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-35000000.0d0)) .or. (.not. (y <= 5.4d-7))) then
        tmp = x * ((z / exp(t)) ** y)
    else
        tmp = x * exp((a * (-z - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -35000000.0) || !(y <= 5.4e-7)) {
		tmp = x * Math.pow((z / Math.exp(t)), y);
	} else {
		tmp = x * Math.exp((a * (-z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -35000000.0) or not (y <= 5.4e-7):
		tmp = x * math.pow((z / math.exp(t)), y)
	else:
		tmp = x * math.exp((a * (-z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -35000000.0) || !(y <= 5.4e-7))
		tmp = Float64(x * (Float64(z / exp(t)) ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -35000000.0) || ~((y <= 5.4e-7)))
		tmp = x * ((z / exp(t)) ^ y);
	else
		tmp = x * exp((a * (-z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -35000000.0], N[Not[LessEqual[y, 5.4e-7]], $MachinePrecision]], N[(x * N[Power[N[(z / N[Exp[t], $MachinePrecision]), $MachinePrecision], y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5e7 or 5.40000000000000018e-7 < y

   1. Initial program 96.9%

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

   3. Taylor expanded in a around 0 90.7%

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

      1. *-commutative 90.7%

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

      2. exp-prod 90.7%

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

      3. exp-diff 90.7%

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

      4. rem-exp-log 90.7%

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

   5. Simplified 90.7%

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

   if -3.5e7 < y < 5.40000000000000018e-7

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0 80.8%

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

      1. sub-neg 80.8%

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

      2. log1p-define 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in z around 0 88.4%

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

      1. +-commutative 88.4%

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

      2. associate-*r* 88.4%

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

      3. associate-*r* 88.4%

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

      4. distribute-lft-out 88.4%

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

      5. mul-1-neg 88.4%

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

   8. Simplified 88.4%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -35000000 \lor \neg \left(y \leq 5.4 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot {\left(\frac{z}{e^{t}}\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+31}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq -10000000 \lor \neg \left(y \leq 8 \cdot 10^{+24}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -2.1e+146)
     t_1
     (if (<= y -1e+31)
       (* x (exp (* t (- y))))
       (if (or (<= y -10000000.0) (not (<= y 8e+24)))
         t_1
         (* x (exp (* a (- (- z) b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -2.1e+146) {
		tmp = t_1;
	} else if (y <= -1e+31) {
		tmp = x * exp((t * -y));
	} else if ((y <= -10000000.0) || !(y <= 8e+24)) {
		tmp = t_1;
	} else {
		tmp = x * exp((a * (-z - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-2.1d+146)) then
        tmp = t_1
    else if (y <= (-1d+31)) then
        tmp = x * exp((t * -y))
    else if ((y <= (-10000000.0d0)) .or. (.not. (y <= 8d+24))) then
        tmp = t_1
    else
        tmp = x * exp((a * (-z - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -2.1e+146) {
		tmp = t_1;
	} else if (y <= -1e+31) {
		tmp = x * Math.exp((t * -y));
	} else if ((y <= -10000000.0) || !(y <= 8e+24)) {
		tmp = t_1;
	} else {
		tmp = x * Math.exp((a * (-z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -2.1e+146:
		tmp = t_1
	elif y <= -1e+31:
		tmp = x * math.exp((t * -y))
	elif (y <= -10000000.0) or not (y <= 8e+24):
		tmp = t_1
	else:
		tmp = x * math.exp((a * (-z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -2.1e+146)
		tmp = t_1;
	elseif (y <= -1e+31)
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	elseif ((y <= -10000000.0) || !(y <= 8e+24))
		tmp = t_1;
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -2.1e+146)
		tmp = t_1;
	elseif (y <= -1e+31)
		tmp = x * exp((t * -y));
	elseif ((y <= -10000000.0) || ~((y <= 8e+24)))
		tmp = t_1;
	else
		tmp = x * exp((a * (-z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+146], t$95$1, If[LessEqual[y, -1e+31], N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -10000000.0], N[Not[LessEqual[y, 8e+24]], $MachinePrecision]], t$95$1, N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1000000000000001e146 or -9.9999999999999996e30 < y < -1e7 or 7.9999999999999999e24 < y

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0 94.7%

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

      1. *-commutative 94.7%

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

      2. exp-prod 94.7%

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

      3. exp-diff 94.7%

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

      4. rem-exp-log 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in t around 0 78.6%

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

   if -2.1000000000000001e146 < y < -9.9999999999999996e30

   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. Add Preprocessing

   3. Taylor expanded in t around inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-lft-neg-out 72.3%

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

      3. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   if -1e7 < y < 7.9999999999999999e24

   1. Initial program 92.0%

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

   3. Taylor expanded in y around 0 78.4%

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

      1. sub-neg 78.4%

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

      2. log1p-define 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in z around 0 86.4%

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

      1. +-commutative 86.4%

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

      2. associate-*r* 86.4%

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

      3. associate-*r* 86.4%

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

      4. distribute-lft-out 86.4%

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

      5. mul-1-neg 86.4%

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

   8. Simplified 86.4%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+146}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+31}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq -10000000 \lor \neg \left(y \leq 8 \cdot 10^{+24}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -2.75 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq -6400000 \lor \neg \left(y \leq 1.2 \cdot 10^{-5}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -2.75e+146)
     t_1
     (if (<= y -1.8e+31)
       (* x (exp (* t (- y))))
       (if (or (<= y -6400000.0) (not (<= y 1.2e-5)))
         t_1
         (* x (exp (* a (- b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -2.75e+146) {
		tmp = t_1;
	} else if (y <= -1.8e+31) {
		tmp = x * exp((t * -y));
	} else if ((y <= -6400000.0) || !(y <= 1.2e-5)) {
		tmp = t_1;
	} else {
		tmp = x * exp((a * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-2.75d+146)) then
        tmp = t_1
    else if (y <= (-1.8d+31)) then
        tmp = x * exp((t * -y))
    else if ((y <= (-6400000.0d0)) .or. (.not. (y <= 1.2d-5))) then
        tmp = t_1
    else
        tmp = x * exp((a * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -2.75e+146) {
		tmp = t_1;
	} else if (y <= -1.8e+31) {
		tmp = x * Math.exp((t * -y));
	} else if ((y <= -6400000.0) || !(y <= 1.2e-5)) {
		tmp = t_1;
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -2.75e+146:
		tmp = t_1
	elif y <= -1.8e+31:
		tmp = x * math.exp((t * -y))
	elif (y <= -6400000.0) or not (y <= 1.2e-5):
		tmp = t_1
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -2.75e+146)
		tmp = t_1;
	elseif (y <= -1.8e+31)
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	elseif ((y <= -6400000.0) || !(y <= 1.2e-5))
		tmp = t_1;
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -2.75e+146)
		tmp = t_1;
	elseif (y <= -1.8e+31)
		tmp = x * exp((t * -y));
	elseif ((y <= -6400000.0) || ~((y <= 1.2e-5)))
		tmp = t_1;
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.75e+146], t$95$1, If[LessEqual[y, -1.8e+31], N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -6400000.0], N[Not[LessEqual[y, 1.2e-5]], $MachinePrecision]], t$95$1, N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7500000000000002e146 or -1.79999999999999998e31 < y < -6.4e6 or 1.2e-5 < y

   1. Initial program 97.0%

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

   3. Taylor expanded in a around 0 93.0%

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

      1. *-commutative 93.0%

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

      2. exp-prod 93.0%

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

      3. exp-diff 93.0%

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

      4. rem-exp-log 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in t around 0 76.1%

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

   if -2.7500000000000002e146 < y < -1.79999999999999998e31

   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. Add Preprocessing

   3. Taylor expanded in t around inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-lft-neg-out 72.3%

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

      3. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   if -6.4e6 < y < 1.2e-5

   1. Initial program 92.4%

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

   3. Taylor expanded in b around inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. distribute-rgt-neg-out 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+146}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq -6400000 \lor \neg \left(y \leq 1.2 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6500000 \lor \neg \left(y \leq 1.2 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6500000.0) (not (<= y 1.2e-5)))
   (* x (pow z y))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6500000.0) || !(y <= 1.2e-5)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp((a * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6500000.0d0)) .or. (.not. (y <= 1.2d-5))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp((a * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6500000.0) || !(y <= 1.2e-5)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6500000.0) or not (y <= 1.2e-5):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6500000.0) || !(y <= 1.2e-5))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6500000.0) || ~((y <= 1.2e-5)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6500000.0], N[Not[LessEqual[y, 1.2e-5]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e6 or 1.2e-5 < y

   1. Initial program 96.9%

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

   3. Taylor expanded in a around 0 90.7%

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

      1. *-commutative 90.7%

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

      2. exp-prod 90.7%

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

      3. exp-diff 90.7%

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

      4. rem-exp-log 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in t around 0 71.3%

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

   if -6.5e6 < y < 1.2e-5

   1. Initial program 92.4%

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

   3. Taylor expanded in b around inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. distribute-rgt-neg-out 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6500000 \lor \neg \left(y \leq 1.2 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9200 \lor \neg \left(y \leq 1.15 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z + b\right) \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9200.0) (not (<= y 1.15e-20)))
   (* x (pow z y))
   (- x (* (+ z b) (* x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9200.0) || !(y <= 1.15e-20)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x - ((z + b) * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9200.0d0)) .or. (.not. (y <= 1.15d-20))) then
        tmp = x * (z ** y)
    else
        tmp = x - ((z + b) * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9200.0) || !(y <= 1.15e-20)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x - ((z + b) * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9200.0) or not (y <= 1.15e-20):
		tmp = x * math.pow(z, y)
	else:
		tmp = x - ((z + b) * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9200.0) || !(y <= 1.15e-20))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x - Float64(Float64(z + b) * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9200.0) || ~((y <= 1.15e-20)))
		tmp = x * (z ^ y);
	else
		tmp = x - ((z + b) * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9200.0], N[Not[LessEqual[y, 1.15e-20]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z + b), $MachinePrecision] * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9200 or 1.15e-20 < y

   1. Initial program 97.0%

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

   3. Taylor expanded in a around 0 88.7%

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

      1. *-commutative 88.7%

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

      2. exp-prod 88.7%

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

      3. exp-diff 88.7%

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

      4. rem-exp-log 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in t around 0 70.7%

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

   if -9200 < y < 1.15e-20

   1. Initial program 92.1%

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

   3. Taylor expanded in y around 0 80.5%

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

      1. sub-neg 80.5%

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

      2. log1p-define 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in z around 0 88.3%

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

      1. +-commutative 88.3%

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

      2. associate-*r* 88.3%

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

      3. associate-*r* 88.3%

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

      4. distribute-lft-out 88.3%

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

      5. mul-1-neg 88.3%

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

   8. Simplified 88.3%

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

   9. Taylor expanded in a around 0 42.4%

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

       1. mul-1-neg 42.4%

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

       2. unsub-neg 42.4%

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

       3. associate-*r* 45.3%

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

       4. *-commutative 45.3%

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

   11. Simplified 45.3%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9200 \lor \neg \left(y \leq 1.15 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z + b\right) \cdot \left(x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 30.9% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+213}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-229}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - x \cdot b\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 350:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.05e+213)
   (- x (* t (* x y)))
   (if (<= y -1.4e-229)
     (* a (- (/ x a) (* x b)))
     (if (<= y 1.8e-267)
       (* b (/ x b))
       (if (<= y 350.0) (- x (* b (* x a))) (* b (* a (- x))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.05e+213) {
		tmp = x - (t * (x * y));
	} else if (y <= -1.4e-229) {
		tmp = a * ((x / a) - (x * b));
	} else if (y <= 1.8e-267) {
		tmp = b * (x / b);
	} else if (y <= 350.0) {
		tmp = x - (b * (x * a));
	} else {
		tmp = b * (a * -x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.05d+213)) then
        tmp = x - (t * (x * y))
    else if (y <= (-1.4d-229)) then
        tmp = a * ((x / a) - (x * b))
    else if (y <= 1.8d-267) then
        tmp = b * (x / b)
    else if (y <= 350.0d0) then
        tmp = x - (b * (x * a))
    else
        tmp = b * (a * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.05e+213) {
		tmp = x - (t * (x * y));
	} else if (y <= -1.4e-229) {
		tmp = a * ((x / a) - (x * b));
	} else if (y <= 1.8e-267) {
		tmp = b * (x / b);
	} else if (y <= 350.0) {
		tmp = x - (b * (x * a));
	} else {
		tmp = b * (a * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.05e+213:
		tmp = x - (t * (x * y))
	elif y <= -1.4e-229:
		tmp = a * ((x / a) - (x * b))
	elif y <= 1.8e-267:
		tmp = b * (x / b)
	elif y <= 350.0:
		tmp = x - (b * (x * a))
	else:
		tmp = b * (a * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.05e+213)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (y <= -1.4e-229)
		tmp = Float64(a * Float64(Float64(x / a) - Float64(x * b)));
	elseif (y <= 1.8e-267)
		tmp = Float64(b * Float64(x / b));
	elseif (y <= 350.0)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	else
		tmp = Float64(b * Float64(a * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.05e+213)
		tmp = x - (t * (x * y));
	elseif (y <= -1.4e-229)
		tmp = a * ((x / a) - (x * b));
	elseif (y <= 1.8e-267)
		tmp = b * (x / b);
	elseif (y <= 350.0)
		tmp = x - (b * (x * a));
	else
		tmp = b * (a * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.05e+213], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-229], N[(a * N[(N[(x / a), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-267], N[(b * N[(x / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 350.0], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.0499999999999999e213

   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. Add Preprocessing

   3. Taylor expanded in t around inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. distribute-lft-neg-out 80.3%

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

      3. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in y around 0 46.1%

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

      1. mul-1-neg 46.1%

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

   8. Simplified 46.1%

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

   if -2.0499999999999999e213 < y < -1.39999999999999995e-229

   1. Initial program 94.8%

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

   3. Taylor expanded in b around inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-rgt-neg-out 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in a around 0 24.9%

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

      1. mul-1-neg 24.9%

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

      2. unsub-neg 24.9%

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

      3. associate-*r* 24.9%

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

      4. *-commutative 24.9%

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

      5. associate-*l* 26.9%

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

   8. Simplified 26.9%

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

   9. Taylor expanded in a around inf 32.1%

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

   if -1.39999999999999995e-229 < y < 1.8000000000000001e-267

   1. Initial program 84.2%

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

   3. Taylor expanded in b around inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. distribute-rgt-neg-out 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in a around 0 31.1%

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

      1. mul-1-neg 31.1%

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

      2. unsub-neg 31.1%

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

      3. associate-*r* 35.4%

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

      4. *-commutative 35.4%

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

      5. associate-*l* 35.4%

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

   8. Simplified 35.4%

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

   9. Taylor expanded in b around inf 43.8%

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

   10. Taylor expanded in b around 0 52.4%

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

   if 1.8000000000000001e-267 < y < 350

   1. Initial program 95.9%

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

   3. Taylor expanded in b around inf 76.1%

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

      1. mul-1-neg 76.1%

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

      2. distribute-rgt-neg-out 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in a around 0 42.4%

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

      1. mul-1-neg 42.4%

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

      2. unsub-neg 42.4%

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

      3. associate-*r* 43.8%

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

      4. *-commutative 43.8%

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

      5. associate-*l* 46.8%

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

   8. Simplified 46.8%

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

   if 350 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 27.5%

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

      1. mul-1-neg 27.5%

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

      2. distribute-rgt-neg-out 27.5%

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

   5. Simplified 27.5%

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

   6. Taylor expanded in a around 0 11.3%

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

      1. mul-1-neg 11.3%

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

      2. unsub-neg 11.3%

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

      3. associate-*r* 12.9%

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

      4. *-commutative 12.9%

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

      5. associate-*l* 12.9%

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

   8. Simplified 12.9%

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

   9. Taylor expanded in b around inf 19.0%

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

   10. Taylor expanded in b around inf 30.9%

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

       1. associate-*r* 30.9%

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

       2. mul-1-neg 30.9%

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

   12. Simplified 30.9%

       \[\leadsto b \cdot \color{blue}{\left(\left(-a\right) \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+213}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-229}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - x \cdot b\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 350:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.1% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+214}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-42}:\\ \;\;\;\;b \cdot \left(a \cdot \left(\frac{x}{a \cdot b} - x\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+48}:\\ \;\;\;\;x - \left(z + b\right) \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.4e+214)
   (- x (* t (* x y)))
   (if (<= y -2.3e-42)
     (* b (* a (- (/ x (* a b)) x)))
     (if (<= y 1.35e+48) (- x (* (+ z b) (* x a))) (* b (* a (- x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.4e+214) {
		tmp = x - (t * (x * y));
	} else if (y <= -2.3e-42) {
		tmp = b * (a * ((x / (a * b)) - x));
	} else if (y <= 1.35e+48) {
		tmp = x - ((z + b) * (x * a));
	} else {
		tmp = b * (a * -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 <= (-5.4d+214)) then
        tmp = x - (t * (x * y))
    else if (y <= (-2.3d-42)) then
        tmp = b * (a * ((x / (a * b)) - x))
    else if (y <= 1.35d+48) then
        tmp = x - ((z + b) * (x * a))
    else
        tmp = b * (a * -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 <= -5.4e+214) {
		tmp = x - (t * (x * y));
	} else if (y <= -2.3e-42) {
		tmp = b * (a * ((x / (a * b)) - x));
	} else if (y <= 1.35e+48) {
		tmp = x - ((z + b) * (x * a));
	} else {
		tmp = b * (a * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.4e+214:
		tmp = x - (t * (x * y))
	elif y <= -2.3e-42:
		tmp = b * (a * ((x / (a * b)) - x))
	elif y <= 1.35e+48:
		tmp = x - ((z + b) * (x * a))
	else:
		tmp = b * (a * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.4e+214)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (y <= -2.3e-42)
		tmp = Float64(b * Float64(a * Float64(Float64(x / Float64(a * b)) - x)));
	elseif (y <= 1.35e+48)
		tmp = Float64(x - Float64(Float64(z + b) * Float64(x * a)));
	else
		tmp = Float64(b * Float64(a * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.4e+214)
		tmp = x - (t * (x * y));
	elseif (y <= -2.3e-42)
		tmp = b * (a * ((x / (a * b)) - x));
	elseif (y <= 1.35e+48)
		tmp = x - ((z + b) * (x * a));
	else
		tmp = b * (a * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.4e+214], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-42], N[(b * N[(a * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+48], N[(x - N[(N[(z + b), $MachinePrecision] * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.40000000000000018e214

   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. Add Preprocessing

   3. Taylor expanded in t around inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. distribute-lft-neg-out 80.3%

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

      3. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in y around 0 46.1%

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

      1. mul-1-neg 46.1%

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

   8. Simplified 46.1%

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

   if -5.40000000000000018e214 < y < -2.30000000000000004e-42

   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. Add Preprocessing

   3. Taylor expanded in b around inf 48.1%

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

      1. mul-1-neg 48.1%

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

      2. distribute-rgt-neg-out 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in a around 0 17.0%

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

      1. mul-1-neg 17.0%

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

      2. unsub-neg 17.0%

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

      3. associate-*r* 16.9%

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

      4. *-commutative 16.9%

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

      5. associate-*l* 17.0%

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

   8. Simplified 17.0%

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

   9. Taylor expanded in b around inf 25.3%

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

   10. Taylor expanded in a around inf 34.0%

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

   if -2.30000000000000004e-42 < y < 1.35000000000000002e48

   1. Initial program 90.8%

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

   3. Taylor expanded in y around 0 76.4%

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

      1. sub-neg 76.4%

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

      2. log1p-define 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in z around 0 85.6%

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

      1. +-commutative 85.6%

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

      2. associate-*r* 85.6%

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

      3. associate-*r* 85.6%

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

      4. distribute-lft-out 85.6%

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

      5. mul-1-neg 85.6%

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

   8. Simplified 85.6%

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

   9. Taylor expanded in a around 0 39.9%

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

       1. mul-1-neg 39.9%

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

       2. unsub-neg 39.9%

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

       3. associate-*r* 42.8%

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

       4. *-commutative 42.8%

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

   11. Simplified 42.8%

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

   if 1.35000000000000002e48 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 27.5%

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

      1. mul-1-neg 27.5%

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

      2. distribute-rgt-neg-out 27.5%

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

   5. Simplified 27.5%

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

   6. Taylor expanded in a around 0 10.8%

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

      1. mul-1-neg 10.8%

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

      2. unsub-neg 10.8%

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

      3. associate-*r* 12.6%

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

      4. *-commutative 12.6%

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

      5. associate-*l* 12.6%

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

   8. Simplified 12.6%

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

   9. Taylor expanded in b around inf 17.9%

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

   10. Taylor expanded in b around inf 33.4%

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

       1. associate-*r* 33.4%

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

       2. mul-1-neg 33.4%

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

   12. Simplified 33.4%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+214}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-42}:\\ \;\;\;\;b \cdot \left(a \cdot \left(\frac{x}{a \cdot b} - x\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+48}:\\ \;\;\;\;x - \left(z + b\right) \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 33.5% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+166}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 350:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4e+166)
   (* t (* x (- y)))
   (if (<= y -1.4e+23)
     (* b (/ x b))
     (if (<= y 350.0) (* x (- 1.0 (* a b))) (* b (* a (- x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4e+166) {
		tmp = t * (x * -y);
	} else if (y <= -1.4e+23) {
		tmp = b * (x / b);
	} else if (y <= 350.0) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = b * (a * -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 <= (-4d+166)) then
        tmp = t * (x * -y)
    else if (y <= (-1.4d+23)) then
        tmp = b * (x / b)
    else if (y <= 350.0d0) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = b * (a * -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 <= -4e+166) {
		tmp = t * (x * -y);
	} else if (y <= -1.4e+23) {
		tmp = b * (x / b);
	} else if (y <= 350.0) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = b * (a * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4e+166:
		tmp = t * (x * -y)
	elif y <= -1.4e+23:
		tmp = b * (x / b)
	elif y <= 350.0:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = b * (a * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4e+166)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= -1.4e+23)
		tmp = Float64(b * Float64(x / b));
	elseif (y <= 350.0)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(b * Float64(a * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4e+166)
		tmp = t * (x * -y);
	elseif (y <= -1.4e+23)
		tmp = b * (x / b);
	elseif (y <= 350.0)
		tmp = x * (1.0 - (a * b));
	else
		tmp = b * (a * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4e+166], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e+23], N[(b * N[(x / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 350.0], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.99999999999999976e166

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf 72.5%

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

      1. mul-1-neg 72.5%

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

      2. distribute-lft-neg-out 72.5%

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

      3. *-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in y around 0 41.1%

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

      1. mul-1-neg 41.1%

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

   8. Simplified 41.1%

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

   9. Taylor expanded in t around inf 41.1%

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

       1. *-commutative 41.1%

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

       2. associate-*r* 33.5%

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

       3. associate-*l* 33.5%

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

       4. *-commutative 33.5%

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

       5. mul-1-neg 33.5%

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

       6. distribute-rgt-neg-in 33.5%

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

   11. Simplified 33.5%

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

   12. Taylor expanded in x around 0 41.1%

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

       1. mul-1-neg 41.1%

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

       2. distribute-rgt-neg-in 41.1%

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

   14. Simplified 41.1%

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

   if -3.99999999999999976e166 < y < -1.4e23

   1. Initial program 97.3%

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

   3. Taylor expanded in b around inf 39.9%

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

      1. mul-1-neg 39.9%

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

      2. distribute-rgt-neg-out 39.9%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in a around 0 5.9%

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

      1. mul-1-neg 5.9%

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

      2. unsub-neg 5.9%

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

      3. associate-*r* 5.8%

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

      4. *-commutative 5.8%

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

      5. associate-*l* 5.8%

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

   8. Simplified 5.8%

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

   9. Taylor expanded in b around inf 21.1%

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

   10. Taylor expanded in b around 0 24.0%

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

   if -1.4e23 < y < 350

   1. Initial program 92.6%

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

   3. Taylor expanded in b around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. distribute-rgt-neg-out 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in a around 0 40.3%

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

      1. mul-1-neg 40.3%

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

      2. unsub-neg 40.3%

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

   8. Simplified 40.3%

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

   if 350 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 27.5%

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

      1. mul-1-neg 27.5%

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

      2. distribute-rgt-neg-out 27.5%

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

   5. Simplified 27.5%

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

   6. Taylor expanded in a around 0 11.3%

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

      1. mul-1-neg 11.3%

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

      2. unsub-neg 11.3%

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

      3. associate-*r* 12.9%

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

      4. *-commutative 12.9%

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

      5. associate-*l* 12.9%

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

   8. Simplified 12.9%

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

   9. Taylor expanded in b around inf 19.0%

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

   10. Taylor expanded in b around inf 30.9%

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

       1. associate-*r* 30.9%

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

       2. mul-1-neg 30.9%

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

   12. Simplified 30.9%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+166}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 350:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 32.7% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+21}:\\ \;\;\;\;b \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 350:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.85e+165)
   (* t (* x (- y)))
   (if (<= y -2.7e+21)
     (* b (/ x b))
     (if (<= y 350.0) (- x (* b (* x a))) (* b (* a (- x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.85e+165) {
		tmp = t * (x * -y);
	} else if (y <= -2.7e+21) {
		tmp = b * (x / b);
	} else if (y <= 350.0) {
		tmp = x - (b * (x * a));
	} else {
		tmp = b * (a * -x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.85d+165)) then
        tmp = t * (x * -y)
    else if (y <= (-2.7d+21)) then
        tmp = b * (x / b)
    else if (y <= 350.0d0) then
        tmp = x - (b * (x * a))
    else
        tmp = b * (a * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.85e+165) {
		tmp = t * (x * -y);
	} else if (y <= -2.7e+21) {
		tmp = b * (x / b);
	} else if (y <= 350.0) {
		tmp = x - (b * (x * a));
	} else {
		tmp = b * (a * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.85e+165:
		tmp = t * (x * -y)
	elif y <= -2.7e+21:
		tmp = b * (x / b)
	elif y <= 350.0:
		tmp = x - (b * (x * a))
	else:
		tmp = b * (a * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.85e+165)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= -2.7e+21)
		tmp = Float64(b * Float64(x / b));
	elseif (y <= 350.0)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	else
		tmp = Float64(b * Float64(a * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.85e+165)
		tmp = t * (x * -y);
	elseif (y <= -2.7e+21)
		tmp = b * (x / b);
	elseif (y <= 350.0)
		tmp = x - (b * (x * a));
	else
		tmp = b * (a * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.85e+165], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e+21], N[(b * N[(x / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 350.0], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.85000000000000013e165

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf 72.5%

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

      1. mul-1-neg 72.5%

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

      2. distribute-lft-neg-out 72.5%

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

      3. *-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in y around 0 41.1%

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

      1. mul-1-neg 41.1%

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

   8. Simplified 41.1%

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

   9. Taylor expanded in t around inf 41.1%

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

       1. *-commutative 41.1%

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

       2. associate-*r* 33.5%

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

       3. associate-*l* 33.5%

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

       4. *-commutative 33.5%

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

       5. mul-1-neg 33.5%

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

       6. distribute-rgt-neg-in 33.5%

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

   11. Simplified 33.5%

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

   12. Taylor expanded in x around 0 41.1%

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

       1. mul-1-neg 41.1%

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

       2. distribute-rgt-neg-in 41.1%

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

   14. Simplified 41.1%

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

   if -2.85000000000000013e165 < y < -2.7e21

   1. Initial program 97.3%

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

   3. Taylor expanded in b around inf 39.9%

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

      1. mul-1-neg 39.9%

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

      2. distribute-rgt-neg-out 39.9%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in a around 0 5.9%

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

      1. mul-1-neg 5.9%

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

      2. unsub-neg 5.9%

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

      3. associate-*r* 5.8%

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

      4. *-commutative 5.8%

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

      5. associate-*l* 5.8%

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

   8. Simplified 5.8%

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

   9. Taylor expanded in b around inf 21.1%

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

   10. Taylor expanded in b around 0 24.0%

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

   if -2.7e21 < y < 350

   1. Initial program 92.6%

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

   3. Taylor expanded in b around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. distribute-rgt-neg-out 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in a around 0 38.9%

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

      1. mul-1-neg 38.9%

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

      2. unsub-neg 38.9%

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

      3. associate-*r* 40.3%

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

      4. *-commutative 40.3%

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

      5. associate-*l* 43.1%

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

   8. Simplified 43.1%

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

   if 350 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 27.5%

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

      1. mul-1-neg 27.5%

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

      2. distribute-rgt-neg-out 27.5%

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

   5. Simplified 27.5%

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

   6. Taylor expanded in a around 0 11.3%

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

      1. mul-1-neg 11.3%

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

      2. unsub-neg 11.3%

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

      3. associate-*r* 12.9%

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

      4. *-commutative 12.9%

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

      5. associate-*l* 12.9%

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

   8. Simplified 12.9%

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

   9. Taylor expanded in b around inf 19.0%

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

   10. Taylor expanded in b around inf 30.9%

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

       1. associate-*r* 30.9%

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

       2. mul-1-neg 30.9%

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

   12. Simplified 30.9%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+21}:\\ \;\;\;\;b \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 350:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.3% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+213}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(\frac{x}{b} - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3e+213)
   (- x (* t (* x y)))
   (if (<= y 1.35e+48) (* b (- (/ x b) (* x a))) (* b (* a (- x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3e+213) {
		tmp = x - (t * (x * y));
	} else if (y <= 1.35e+48) {
		tmp = b * ((x / b) - (x * a));
	} else {
		tmp = b * (a * -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 <= (-3d+213)) then
        tmp = x - (t * (x * y))
    else if (y <= 1.35d+48) then
        tmp = b * ((x / b) - (x * a))
    else
        tmp = b * (a * -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 <= -3e+213) {
		tmp = x - (t * (x * y));
	} else if (y <= 1.35e+48) {
		tmp = b * ((x / b) - (x * a));
	} else {
		tmp = b * (a * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3e+213:
		tmp = x - (t * (x * y))
	elif y <= 1.35e+48:
		tmp = b * ((x / b) - (x * a))
	else:
		tmp = b * (a * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3e+213)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (y <= 1.35e+48)
		tmp = Float64(b * Float64(Float64(x / b) - Float64(x * a)));
	else
		tmp = Float64(b * Float64(a * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3e+213)
		tmp = x - (t * (x * y));
	elseif (y <= 1.35e+48)
		tmp = b * ((x / b) - (x * a));
	else
		tmp = b * (a * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3e+213], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+48], N[(b * N[(N[(x / b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0000000000000001e213

   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. Add Preprocessing

   3. Taylor expanded in t around inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. distribute-lft-neg-out 80.3%

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

      3. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in y around 0 46.1%

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

      1. mul-1-neg 46.1%

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

   8. Simplified 46.1%

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

   if -3.0000000000000001e213 < y < 1.35000000000000002e48

   1. Initial program 93.0%

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

   3. Taylor expanded in b around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. distribute-rgt-neg-out 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in a around 0 31.3%

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

      1. mul-1-neg 31.3%

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

      2. unsub-neg 31.3%

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

      3. associate-*r* 32.3%

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

      4. *-commutative 32.3%

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

      5. associate-*l* 34.3%

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

   8. Simplified 34.3%

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

   9. Taylor expanded in b around inf 36.9%

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

   if 1.35000000000000002e48 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 27.5%

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

      1. mul-1-neg 27.5%

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

      2. distribute-rgt-neg-out 27.5%

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

   5. Simplified 27.5%

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

   6. Taylor expanded in a around 0 10.8%

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

      1. mul-1-neg 10.8%

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

      2. unsub-neg 10.8%

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

      3. associate-*r* 12.6%

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

      4. *-commutative 12.6%

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

      5. associate-*l* 12.6%

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

   8. Simplified 12.6%

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

   9. Taylor expanded in b around inf 17.9%

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

   10. Taylor expanded in b around inf 33.4%

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

       1. associate-*r* 33.4%

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

       2. mul-1-neg 33.4%

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

   12. Simplified 33.4%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+213}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(\frac{x}{b} - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.5% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+22}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;y \leq 46000:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.9e+22)
   (- x (* x (* y t)))
   (if (<= y 46000.0) (- x (* b (* x a))) (* b (* a (- x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.9e+22) {
		tmp = x - (x * (y * t));
	} else if (y <= 46000.0) {
		tmp = x - (b * (x * a));
	} else {
		tmp = b * (a * -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 <= (-3.9d+22)) then
        tmp = x - (x * (y * t))
    else if (y <= 46000.0d0) then
        tmp = x - (b * (x * a))
    else
        tmp = b * (a * -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 <= -3.9e+22) {
		tmp = x - (x * (y * t));
	} else if (y <= 46000.0) {
		tmp = x - (b * (x * a));
	} else {
		tmp = b * (a * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.9e+22:
		tmp = x - (x * (y * t))
	elif y <= 46000.0:
		tmp = x - (b * (x * a))
	else:
		tmp = b * (a * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.9e+22)
		tmp = Float64(x - Float64(x * Float64(y * t)));
	elseif (y <= 46000.0)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	else
		tmp = Float64(b * Float64(a * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.9e+22)
		tmp = x - (x * (y * t));
	elseif (y <= 46000.0)
		tmp = x - (b * (x * a));
	else
		tmp = b * (a * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.9e+22], N[(x - N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 46000.0], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.90000000000000021e22

   1. Initial program 96.8%

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

   3. Taylor expanded in t around inf 68.6%

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

      1. mul-1-neg 68.6%

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

      2. distribute-lft-neg-out 68.6%

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

      3. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in y around 0 24.3%

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

      1. mul-1-neg 24.3%

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

      2. unsub-neg 24.3%

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

      3. *-commutative 24.3%

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

      4. associate-*l* 24.5%

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

      5. *-commutative 24.5%

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

   8. Simplified 24.5%

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

   if -3.90000000000000021e22 < y < 46000

   1. Initial program 92.6%

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

   3. Taylor expanded in b around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. distribute-rgt-neg-out 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in a around 0 38.9%

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

      1. mul-1-neg 38.9%

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

      2. unsub-neg 38.9%

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

      3. associate-*r* 40.3%

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

      4. *-commutative 40.3%

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

      5. associate-*l* 43.1%

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

   8. Simplified 43.1%

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

   if 46000 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 27.5%

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

      1. mul-1-neg 27.5%

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

      2. distribute-rgt-neg-out 27.5%

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

   5. Simplified 27.5%

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

   6. Taylor expanded in a around 0 11.3%

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

      1. mul-1-neg 11.3%

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

      2. unsub-neg 11.3%

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

      3. associate-*r* 12.9%

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

      4. *-commutative 12.9%

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

      5. associate-*l* 12.9%

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

   8. Simplified 12.9%

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

   9. Taylor expanded in b around inf 19.0%

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

   10. Taylor expanded in b around inf 30.9%

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

       1. associate-*r* 30.9%

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

       2. mul-1-neg 30.9%

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

   12. Simplified 30.9%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+22}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;y \leq 46000:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.3% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+168}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.8e+168)
   (* t (* x (- y)))
   (if (<= y 1.35e+48) (* b (/ x b)) (* b (* a (- x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.8e+168) {
		tmp = t * (x * -y);
	} else if (y <= 1.35e+48) {
		tmp = b * (x / b);
	} else {
		tmp = b * (a * -x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.8d+168)) then
        tmp = t * (x * -y)
    else if (y <= 1.35d+48) then
        tmp = b * (x / b)
    else
        tmp = b * (a * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.8e+168) {
		tmp = t * (x * -y);
	} else if (y <= 1.35e+48) {
		tmp = b * (x / b);
	} else {
		tmp = b * (a * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.8e+168:
		tmp = t * (x * -y)
	elif y <= 1.35e+48:
		tmp = b * (x / b)
	else:
		tmp = b * (a * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.8e+168)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 1.35e+48)
		tmp = Float64(b * Float64(x / b));
	else
		tmp = Float64(b * Float64(a * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.8e+168)
		tmp = t * (x * -y);
	elseif (y <= 1.35e+48)
		tmp = b * (x / b);
	else
		tmp = b * (a * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.8e+168], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+48], N[(b * N[(x / b), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000019e168

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf 72.5%

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

      1. mul-1-neg 72.5%

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

      2. distribute-lft-neg-out 72.5%

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

      3. *-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in y around 0 41.1%

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

      1. mul-1-neg 41.1%

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

   8. Simplified 41.1%

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

   9. Taylor expanded in t around inf 41.1%

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

       1. *-commutative 41.1%

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

       2. associate-*r* 33.5%

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

       3. associate-*l* 33.5%

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

       4. *-commutative 33.5%

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

       5. mul-1-neg 33.5%

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

       6. distribute-rgt-neg-in 33.5%

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

   11. Simplified 33.5%

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

   12. Taylor expanded in x around 0 41.1%

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

       1. mul-1-neg 41.1%

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

       2. distribute-rgt-neg-in 41.1%

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

   14. Simplified 41.1%

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

   if -4.80000000000000019e168 < y < 1.35000000000000002e48

   1. Initial program 92.8%

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

   3. Taylor expanded in b around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. distribute-rgt-neg-out 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in a around 0 31.0%

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

      1. mul-1-neg 31.0%

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

      2. unsub-neg 31.0%

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

      3. associate-*r* 32.0%

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

      4. *-commutative 32.0%

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

      5. associate-*l* 34.1%

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

   8. Simplified 34.1%

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

   9. Taylor expanded in b around inf 36.8%

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

   10. Taylor expanded in b around 0 31.9%

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

   if 1.35000000000000002e48 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 27.5%

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

      1. mul-1-neg 27.5%

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

      2. distribute-rgt-neg-out 27.5%

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

   5. Simplified 27.5%

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

   6. Taylor expanded in a around 0 10.8%

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

      1. mul-1-neg 10.8%

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

      2. unsub-neg 10.8%

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

      3. associate-*r* 12.6%

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

      4. *-commutative 12.6%

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

      5. associate-*l* 12.6%

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

   8. Simplified 12.6%

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

   9. Taylor expanded in b around inf 17.9%

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

   10. Taylor expanded in b around inf 33.4%

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

       1. associate-*r* 33.4%

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

       2. mul-1-neg 33.4%

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

   12. Simplified 33.4%

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

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+168}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 27.0% accurate, 28.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.8e+51) (* b (/ x b)) (* b (* a (- x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.8e+51) {
		tmp = b * (x / b);
	} else {
		tmp = b * (a * -x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.8d+51) then
        tmp = b * (x / b)
    else
        tmp = b * (a * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.8e+51) {
		tmp = b * (x / b);
	} else {
		tmp = b * (a * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.8e+51:
		tmp = b * (x / b)
	else:
		tmp = b * (a * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.8e+51)
		tmp = Float64(b * Float64(x / b));
	else
		tmp = Float64(b * Float64(a * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.8e+51)
		tmp = b * (x / b);
	else
		tmp = b * (a * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.8e+51], N[(b * N[(x / b), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.80000000000000005e51

   1. Initial program 93.2%

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

   3. Taylor expanded in b around inf 62.4%

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

      1. mul-1-neg 62.4%

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

      2. distribute-rgt-neg-out 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in a around 0 28.5%

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

      1. mul-1-neg 28.5%

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

      2. unsub-neg 28.5%

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

      3. associate-*r* 29.4%

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

      4. *-commutative 29.4%

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

      5. associate-*l* 31.2%

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

   8. Simplified 31.2%

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

   9. Taylor expanded in b around inf 34.0%

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

   10. Taylor expanded in b around 0 28.9%

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

   if 1.80000000000000005e51 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 27.5%

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

      1. mul-1-neg 27.5%

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

      2. distribute-rgt-neg-out 27.5%

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

   5. Simplified 27.5%

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

   6. Taylor expanded in a around 0 10.8%

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

      1. mul-1-neg 10.8%

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

      2. unsub-neg 10.8%

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

      3. associate-*r* 12.6%

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

      4. *-commutative 12.6%

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

      5. associate-*l* 12.6%

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

   8. Simplified 12.6%

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

   9. Taylor expanded in b around inf 17.9%

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

   10. Taylor expanded in b around inf 33.4%

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

       1. associate-*r* 33.4%

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

       2. mul-1-neg 33.4%

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

   12. Simplified 33.4%

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

4. Final simplification 29.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 24.9% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ b \cdot \frac{x}{b} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return b * (x / 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 = b * (x / b)
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	return Float64(b * Float64(x / b))
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(b * N[(x / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.6%

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

3. Taylor expanded in b around inf 55.3%

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

   1. mul-1-neg 55.3%

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

   2. distribute-rgt-neg-out 55.3%

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

5. Simplified 55.3%

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

6. Taylor expanded in a around 0 24.9%

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

   1. mul-1-neg 24.9%

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

   2. unsub-neg 24.9%

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

   3. associate-*r* 26.0%

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

   4. *-commutative 26.0%

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

   5. associate-*l* 27.4%

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

8. Simplified 27.4%

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

9. Taylor expanded in b around inf 30.7%

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

10. Taylor expanded in b around 0 25.9%

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

11. Final simplification 25.9%

    \[\leadsto b \cdot \frac{x}{b} \]
12. Add Preprocessing

Alternative 17: 19.2% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

3. Taylor expanded in b around inf 55.3%

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

   1. mul-1-neg 55.3%

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

   2. distribute-rgt-neg-out 55.3%

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

5. Simplified 55.3%

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

6. Taylor expanded in a around 0 16.5%

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

7. Final simplification 16.5%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(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))))))