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

Percentage Accurate: 96.7% → 99.7%

Time: 19.0s

Alternatives: 17

Speedup: 1.0×

• 21.2% 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: 96.7% 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: 99.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. +-commutative 97.7%

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

   2. fma-def 98.1%

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

   3. sub-neg 98.1%

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

   4. log1p-def 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 96.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

2. Final simplification 97.7%

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

Alternative 3: 85.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-156} \lor \neg \left(y \leq 3.9 \cdot 10^{-44}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.05e-156) (not (<= y 3.9e-44)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (- z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e-156) || !(y <= 3.9e-44)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * (-z - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.05d-156)) .or. (.not. (y <= 3.9d-44))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((a * (-z - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e-156) || !(y <= 3.9e-44)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * (-z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.05e-156) or not (y <= 3.9e-44):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * (-z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.05e-156) || !(y <= 3.9e-44))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	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 <= -1.05e-156) || ~((y <= 3.9e-44)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((a * (-z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.05e-156], N[Not[LessEqual[y, 3.9e-44]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05000000000000006e-156 or 3.9000000000000002e-44 < y

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 83.5%

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

   if -1.05000000000000006e-156 < y < 3.9000000000000002e-44

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 89.9%

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

      1. sub-neg 89.9%

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

      2. neg-mul-1 89.9%

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

      3. log1p-def 93.7%

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

      4. neg-mul-1 93.7%

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

   4. Simplified 93.7%

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

   5. Taylor expanded in z around 0 93.7%

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

      1. associate-*r* 93.7%

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

      2. associate-*r* 93.7%

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

      3. distribute-lft-out 93.7%

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

      4. neg-mul-1 93.7%

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

   7. Simplified 93.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-156} \lor \neg \left(y \leq 3.9 \cdot 10^{-44}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \]

Alternative 4: 72.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \lor \neg \left(y \leq 1.8 \cdot 10^{+60}\right) \land \left(y \leq 2.2 \cdot 10^{+142} \lor \neg \left(y \leq 1.9 \cdot 10^{+172}\right)\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{-a \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.8)
         (and (not (<= y 1.8e+60)) (or (<= y 2.2e+142) (not (<= y 1.9e+172)))))
   (* 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 <= -3.8) || (!(y <= 1.8e+60) && ((y <= 2.2e+142) || !(y <= 1.9e+172)))) {
		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 <= (-3.8d0)) .or. (.not. (y <= 1.8d+60)) .and. (y <= 2.2d+142) .or. (.not. (y <= 1.9d+172))) 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 <= -3.8) || (!(y <= 1.8e+60) && ((y <= 2.2e+142) || !(y <= 1.9e+172)))) {
		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 <= -3.8) or (not (y <= 1.8e+60) and ((y <= 2.2e+142) or not (y <= 1.9e+172))):
		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 <= -3.8) || (!(y <= 1.8e+60) && ((y <= 2.2e+142) || !(y <= 1.9e+172))))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(-Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.8) || (~((y <= 1.8e+60)) && ((y <= 2.2e+142) || ~((y <= 1.9e+172)))))
		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, -3.8], And[N[Not[LessEqual[y, 1.8e+60]], $MachinePrecision], Or[LessEqual[y, 2.2e+142], N[Not[LessEqual[y, 1.9e+172]], $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 < -3.7999999999999998 or 1.79999999999999984e60 < y < 2.19999999999999987e142 or 1.89999999999999985e172 < y

   1. Initial program 97.5%

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

   2. Taylor expanded in y around inf 87.5%

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

   3. Taylor expanded in t around 0 70.8%

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

   if -3.7999999999999998 < y < 1.79999999999999984e60 or 2.19999999999999987e142 < y < 1.89999999999999985e172

   1. Initial program 97.9%

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

   2. Taylor expanded in b around inf 78.4%

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

      1. associate-*r* 78.4%

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

      2. *-commutative 78.4%

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

      3. neg-mul-1 78.4%

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

   4. Simplified 78.4%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \lor \neg \left(y \leq 1.8 \cdot 10^{+60}\right) \land \left(y \leq 2.2 \cdot 10^{+142} \lor \neg \left(y \leq 1.9 \cdot 10^{+172}\right)\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{-a \cdot b}\\ \end{array} \]

Alternative 5: 72.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -220:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-43}:\\ \;\;\;\;x \cdot e^{-a \cdot b}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+181} \lor \neg \left(y \leq 4.3 \cdot 10^{+250}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -220.0)
     t_1
     (if (<= y 2.3e-43)
       (* x (exp (- (* a b))))
       (if (or (<= y 6e+181) (not (<= y 4.3e+250)))
         (* x (exp (* t (- y))))
         t_1)))))

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 <= -220.0) {
		tmp = t_1;
	} else if (y <= 2.3e-43) {
		tmp = x * exp(-(a * b));
	} else if ((y <= 6e+181) || !(y <= 4.3e+250)) {
		tmp = x * exp((t * -y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-220.0d0)) then
        tmp = t_1
    else if (y <= 2.3d-43) then
        tmp = x * exp(-(a * b))
    else if ((y <= 6d+181) .or. (.not. (y <= 4.3d+250))) then
        tmp = x * exp((t * -y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -220.0) {
		tmp = t_1;
	} else if (y <= 2.3e-43) {
		tmp = x * Math.exp(-(a * b));
	} else if ((y <= 6e+181) || !(y <= 4.3e+250)) {
		tmp = x * Math.exp((t * -y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -220.0:
		tmp = t_1
	elif y <= 2.3e-43:
		tmp = x * math.exp(-(a * b))
	elif (y <= 6e+181) or not (y <= 4.3e+250):
		tmp = x * math.exp((t * -y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -220.0)
		tmp = t_1;
	elseif (y <= 2.3e-43)
		tmp = Float64(x * exp(Float64(-Float64(a * b))));
	elseif ((y <= 6e+181) || !(y <= 4.3e+250))
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	else
		tmp = t_1;
	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 <= -220.0)
		tmp = t_1;
	elseif (y <= 2.3e-43)
		tmp = x * exp(-(a * b));
	elseif ((y <= 6e+181) || ~((y <= 4.3e+250)))
		tmp = x * exp((t * -y));
	else
		tmp = t_1;
	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, -220.0], t$95$1, If[LessEqual[y, 2.3e-43], N[(x * N[Exp[(-N[(a * b), $MachinePrecision])], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 6e+181], N[Not[LessEqual[y, 4.3e+250]], $MachinePrecision]], N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -220 or 6.00000000000000024e181 < y < 4.3e250

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 87.0%

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

   3. Taylor expanded in t around 0 73.9%

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

   if -220 < y < 2.2999999999999999e-43

   1. Initial program 97.4%

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

   2. Taylor expanded in b around inf 82.0%

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

      1. associate-*r* 82.0%

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

      2. *-commutative 82.0%

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

      3. neg-mul-1 82.0%

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

   4. Simplified 82.0%

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

   if 2.2999999999999999e-43 < y < 6.00000000000000024e181 or 4.3e250 < y

   1. Initial program 98.4%

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

   2. Taylor expanded in t around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. distribute-rgt-neg-out 74.1%

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

   4. Simplified 74.1%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -220:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-43}:\\ \;\;\;\;x \cdot e^{-a \cdot b}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+181} \lor \neg \left(y \leq 4.3 \cdot 10^{+250}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 6: 74.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -23500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-43}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+181} \lor \neg \left(y \leq 9 \cdot 10^{+249}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -23500000000000.0)
     t_1
     (if (<= y 2.8e-43)
       (* x (exp (* a (- (- z) b))))
       (if (or (<= y 9e+181) (not (<= y 9e+249)))
         (* x (exp (* t (- y))))
         t_1)))))

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 <= -23500000000000.0) {
		tmp = t_1;
	} else if (y <= 2.8e-43) {
		tmp = x * exp((a * (-z - b)));
	} else if ((y <= 9e+181) || !(y <= 9e+249)) {
		tmp = x * exp((t * -y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-23500000000000.0d0)) then
        tmp = t_1
    else if (y <= 2.8d-43) then
        tmp = x * exp((a * (-z - b)))
    else if ((y <= 9d+181) .or. (.not. (y <= 9d+249))) then
        tmp = x * exp((t * -y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -23500000000000.0) {
		tmp = t_1;
	} else if (y <= 2.8e-43) {
		tmp = x * Math.exp((a * (-z - b)));
	} else if ((y <= 9e+181) || !(y <= 9e+249)) {
		tmp = x * Math.exp((t * -y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -23500000000000.0:
		tmp = t_1
	elif y <= 2.8e-43:
		tmp = x * math.exp((a * (-z - b)))
	elif (y <= 9e+181) or not (y <= 9e+249):
		tmp = x * math.exp((t * -y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -23500000000000.0)
		tmp = t_1;
	elseif (y <= 2.8e-43)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	elseif ((y <= 9e+181) || !(y <= 9e+249))
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	else
		tmp = t_1;
	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 <= -23500000000000.0)
		tmp = t_1;
	elseif (y <= 2.8e-43)
		tmp = x * exp((a * (-z - b)));
	elseif ((y <= 9e+181) || ~((y <= 9e+249)))
		tmp = x * exp((t * -y));
	else
		tmp = t_1;
	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, -23500000000000.0], t$95$1, If[LessEqual[y, 2.8e-43], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 9e+181], N[Not[LessEqual[y, 9e+249]], $MachinePrecision]], N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.35e13 or 9e181 < y < 8.9999999999999993e249

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 86.8%

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

   3. Taylor expanded in t around 0 73.6%

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

   if -2.35e13 < y < 2.7999999999999998e-43

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 81.3%

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

      1. sub-neg 81.3%

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

      2. neg-mul-1 81.3%

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

      3. log1p-def 85.6%

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

      4. neg-mul-1 85.6%

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

   4. Simplified 85.6%

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

   5. Taylor expanded in z around 0 85.6%

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

      1. associate-*r* 85.6%

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

      2. associate-*r* 85.6%

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

      3. distribute-lft-out 85.6%

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

      4. neg-mul-1 85.6%

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

   7. Simplified 85.6%

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

   if 2.7999999999999998e-43 < y < 9e181 or 8.9999999999999993e249 < y

   1. Initial program 98.4%

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

   2. Taylor expanded in t around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. distribute-rgt-neg-out 74.1%

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

   4. Simplified 74.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -23500000000000:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-43}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+181} \lor \neg \left(y \leq 9 \cdot 10^{+249}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 7: 53.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7000000000000:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+184} \lor \neg \left(t \leq 1.6 \cdot 10^{+236}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - \left(y \cdot y\right) \cdot \left(t \cdot t\right)}{\frac{y \cdot t + 1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7000000000000.0)
   (* x (- 1.0 (* y t)))
   (if (or (<= t 4e+184) (not (<= t 1.6e+236)))
     (* x (pow z y))
     (/ (- 1.0 (* (* y y) (* t t))) (/ (+ (* y t) 1.0) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7000000000000.0) {
		tmp = x * (1.0 - (y * t));
	} else if ((t <= 4e+184) || !(t <= 1.6e+236)) {
		tmp = x * pow(z, y);
	} else {
		tmp = (1.0 - ((y * y) * (t * t))) / (((y * t) + 1.0) / 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 (t <= (-7000000000000.0d0)) then
        tmp = x * (1.0d0 - (y * t))
    else if ((t <= 4d+184) .or. (.not. (t <= 1.6d+236))) then
        tmp = x * (z ** y)
    else
        tmp = (1.0d0 - ((y * y) * (t * t))) / (((y * t) + 1.0d0) / 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 (t <= -7000000000000.0) {
		tmp = x * (1.0 - (y * t));
	} else if ((t <= 4e+184) || !(t <= 1.6e+236)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = (1.0 - ((y * y) * (t * t))) / (((y * t) + 1.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7000000000000.0:
		tmp = x * (1.0 - (y * t))
	elif (t <= 4e+184) or not (t <= 1.6e+236):
		tmp = x * math.pow(z, y)
	else:
		tmp = (1.0 - ((y * y) * (t * t))) / (((y * t) + 1.0) / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7000000000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif ((t <= 4e+184) || !(t <= 1.6e+236))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(Float64(1.0 - Float64(Float64(y * y) * Float64(t * t))) / Float64(Float64(Float64(y * t) + 1.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7000000000000.0)
		tmp = x * (1.0 - (y * t));
	elseif ((t <= 4e+184) || ~((t <= 1.6e+236)))
		tmp = x * (z ^ y);
	else
		tmp = (1.0 - ((y * y) * (t * t))) / (((y * t) + 1.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7000000000000.0], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 4e+184], N[Not[LessEqual[t, 1.6e+236]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[(N[(y * y), $MachinePrecision] * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * t), $MachinePrecision] + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7e12

   1. Initial program 98.4%

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

   2. Taylor expanded in t around inf 84.1%

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

      1. mul-1-neg 84.1%

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

      2. distribute-rgt-neg-out 84.1%

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

   4. Simplified 84.1%

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

   5. Taylor expanded in y around 0 36.7%

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

      1. +-commutative 36.7%

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

      2. mul-1-neg 36.7%

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

      3. unsub-neg 36.7%

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

      4. *-commutative 36.7%

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

   7. Simplified 36.7%

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

   if -7e12 < t < 4.00000000000000007e184 or 1.6000000000000001e236 < t

   1. Initial program 97.4%

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

   2. Taylor expanded in y around inf 66.9%

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

   3. Taylor expanded in t around 0 61.9%

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

   if 4.00000000000000007e184 < t < 1.6000000000000001e236

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. distribute-rgt-neg-out 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in y around 0 4.2%

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

      1. +-commutative 4.2%

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

      2. mul-1-neg 4.2%

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

      3. unsub-neg 4.2%

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

      4. *-commutative 4.2%

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

   7. Simplified 4.2%

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

      1. distribute-rgt-out-- 4.2%

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

      2. *-un-lft-identity 4.2%

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

      3. *-commutative 4.2%

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

      4. associate-*r* 19.5%

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

      5. sub-neg 19.5%

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

      6. flip-+ 18.5%

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

      7. distribute-rgt-neg-in 18.5%

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

      8. *-commutative 18.5%

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

      9. distribute-rgt-neg-in 18.5%

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

      10. *-commutative 18.5%

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

      11. distribute-rgt-neg-in 18.5%

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

      12. *-commutative 18.5%

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

   9. Applied egg-rr 18.5%

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

   10. Taylor expanded in x around 0 83.3%

       \[\leadsto \color{blue}{\frac{\left(1 - {y}^{2} \cdot {t}^{2}\right) \cdot x}{1 - -1 \cdot \left(y \cdot t\right)}} \]
   11. Step-by-step derivation

       1. associate-/l* 83.3%

          \[\leadsto \color{blue}{\frac{1 - {y}^{2} \cdot {t}^{2}}{\frac{1 - -1 \cdot \left(y \cdot t\right)}{x}}} \]

       2. sub-neg 83.3%

          \[\leadsto \frac{1 - {y}^{2} \cdot {t}^{2}}{\frac{\color{blue}{1 + \left(--1 \cdot \left(y \cdot t\right)\right)}}{x}} \]

       3. mul-1-neg 83.3%

          \[\leadsto \frac{1 - {y}^{2} \cdot {t}^{2}}{\frac{1 + \left(-\color{blue}{\left(-y \cdot t\right)}\right)}{x}} \]

       4. *-commutative 83.3%

          \[\leadsto \frac{1 - {y}^{2} \cdot {t}^{2}}{\frac{1 + \left(-\left(-\color{blue}{t \cdot y}\right)\right)}{x}} \]

       5. remove-double-neg 83.3%

          \[\leadsto \frac{1 - {y}^{2} \cdot {t}^{2}}{\frac{1 + \color{blue}{t \cdot y}}{x}} \]

       6. *-commutative 83.3%

          \[\leadsto \frac{1 - {y}^{2} \cdot {t}^{2}}{\frac{1 + \color{blue}{y \cdot t}}{x}} \]

       7. unpow2 83.3%

          \[\leadsto \frac{1 - \color{blue}{\left(y \cdot y\right)} \cdot {t}^{2}}{\frac{1 + y \cdot t}{x}} \]

       8. unpow2 83.3%

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

       9. *-commutative 83.3%

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

       10. *-lft-identity 83.3%

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

       11. metadata-eval 83.3%

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

       12. *-commutative 83.3%

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

       13. cancel-sign-sub-inv 83.3%

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

       14. mul-1-neg 83.3%

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

   12. Simplified 83.3%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7000000000000:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+184} \lor \neg \left(t \leq 1.6 \cdot 10^{+236}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - \left(y \cdot y\right) \cdot \left(t \cdot t\right)}{\frac{y \cdot t + 1}{x}}\\ \end{array} \]

Alternative 8: 30.9% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(x \cdot t\right)\\ t_2 := \frac{x \cdot x}{t_1}\\ \mathbf{if}\;b \leq -260000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+280}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot y\right) \cdot \left(\left(t \cdot t\right) \cdot \left(-x \cdot x\right)\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (* x t)))) (t_2 (/ (* x x) t_1)))
   (if (<= b -260000000.0)
     t_2
     (if (<= b 9e-14)
       (* x (- 1.0 (* y t)))
       (if (<= b 1.16e+70)
         t_2
         (if (<= b 1.15e+280)
           (* x (- 1.0 (* a b)))
           (/ (* (* y y) (* (* t t) (- (* x x)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (x * t));
	double t_2 = (x * x) / t_1;
	double tmp;
	if (b <= -260000000.0) {
		tmp = t_2;
	} else if (b <= 9e-14) {
		tmp = x * (1.0 - (y * t));
	} else if (b <= 1.16e+70) {
		tmp = t_2;
	} else if (b <= 1.15e+280) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = ((y * y) * ((t * t) * -(x * x))) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (x * t))
    t_2 = (x * x) / t_1
    if (b <= (-260000000.0d0)) then
        tmp = t_2
    else if (b <= 9d-14) then
        tmp = x * (1.0d0 - (y * t))
    else if (b <= 1.16d+70) then
        tmp = t_2
    else if (b <= 1.15d+280) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = ((y * y) * ((t * t) * -(x * x))) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (x * t));
	double t_2 = (x * x) / t_1;
	double tmp;
	if (b <= -260000000.0) {
		tmp = t_2;
	} else if (b <= 9e-14) {
		tmp = x * (1.0 - (y * t));
	} else if (b <= 1.16e+70) {
		tmp = t_2;
	} else if (b <= 1.15e+280) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = ((y * y) * ((t * t) * -(x * x))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (x * t))
	t_2 = (x * x) / t_1
	tmp = 0
	if b <= -260000000.0:
		tmp = t_2
	elif b <= 9e-14:
		tmp = x * (1.0 - (y * t))
	elif b <= 1.16e+70:
		tmp = t_2
	elif b <= 1.15e+280:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = ((y * y) * ((t * t) * -(x * x))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(x * t)))
	t_2 = Float64(Float64(x * x) / t_1)
	tmp = 0.0
	if (b <= -260000000.0)
		tmp = t_2;
	elseif (b <= 9e-14)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif (b <= 1.16e+70)
		tmp = t_2;
	elseif (b <= 1.15e+280)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(Float64(Float64(y * y) * Float64(Float64(t * t) * Float64(-Float64(x * x)))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (x * t));
	t_2 = (x * x) / t_1;
	tmp = 0.0;
	if (b <= -260000000.0)
		tmp = t_2;
	elseif (b <= 9e-14)
		tmp = x * (1.0 - (y * t));
	elseif (b <= 1.16e+70)
		tmp = t_2;
	elseif (b <= 1.15e+280)
		tmp = x * (1.0 - (a * b));
	else
		tmp = ((y * y) * ((t * t) * -(x * x))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * x), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[b, -260000000.0], t$95$2, If[LessEqual[b, 9e-14], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.16e+70], t$95$2, If[LessEqual[b, 1.15e+280], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * y), $MachinePrecision] * N[(N[(t * t), $MachinePrecision] * (-N[(x * x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.6e8 or 8.9999999999999995e-14 < b < 1.1599999999999999e70

   1. Initial program 98.8%

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

   2. Taylor expanded in t around inf 43.9%

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

      1. mul-1-neg 43.9%

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

      2. distribute-rgt-neg-out 43.9%

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

   4. Simplified 43.9%

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

   5. Taylor expanded in y around 0 16.5%

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

      1. +-commutative 16.5%

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

      2. mul-1-neg 16.5%

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

      3. unsub-neg 16.5%

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

      4. *-commutative 16.5%

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

   7. Simplified 16.5%

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

      1. distribute-rgt-out-- 16.5%

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

      2. *-un-lft-identity 16.5%

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

      3. *-commutative 16.5%

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

      4. associate-*r* 17.6%

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

      5. sub-neg 17.6%

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

      6. flip-+ 21.2%

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

      7. distribute-rgt-neg-in 21.2%

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

      8. *-commutative 21.2%

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

      9. distribute-rgt-neg-in 21.2%

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

      10. *-commutative 21.2%

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

      11. distribute-rgt-neg-in 21.2%

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

      12. *-commutative 21.2%

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

   9. Applied egg-rr 21.2%

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

   10. Taylor expanded in y around 0 37.4%

       \[\leadsto \frac{\color{blue}{{x}^{2}}}{x - y \cdot \left(-x \cdot t\right)} \]
   11. Step-by-step derivation

       1. unpow2 37.4%

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

   12. Simplified 37.4%

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

   if -2.6e8 < b < 8.9999999999999995e-14

   1. Initial program 96.6%

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

   2. Taylor expanded in t around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-rgt-neg-out 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in y around 0 41.7%

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

      1. +-commutative 41.7%

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

      2. mul-1-neg 41.7%

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

      3. unsub-neg 41.7%

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

      4. *-commutative 41.7%

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

   7. Simplified 41.7%

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

   if 1.1599999999999999e70 < b < 1.15e280

   1. Initial program 97.8%

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

   2. Taylor expanded in b around inf 77.1%

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

      1. associate-*r* 77.1%

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

      2. *-commutative 77.1%

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

      3. neg-mul-1 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in b around 0 33.7%

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

      1. mul-1-neg 33.7%

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

      2. unsub-neg 33.7%

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

      3. *-commutative 33.7%

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

   7. Simplified 33.7%

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

   if 1.15e280 < b

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 26.2%

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

      1. mul-1-neg 26.2%

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

      2. distribute-rgt-neg-out 26.2%

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

   4. Simplified 26.2%

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

   5. Taylor expanded in y around 0 4.7%

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

      1. +-commutative 4.7%

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

      2. mul-1-neg 4.7%

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

      3. unsub-neg 4.7%

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

      4. *-commutative 4.7%

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

   7. Simplified 4.7%

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

      1. distribute-rgt-out-- 4.7%

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

      2. *-un-lft-identity 4.7%

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

      3. *-commutative 4.7%

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

      4. associate-*r* 4.7%

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

      5. sub-neg 4.7%

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

      6. flip-+ 46.1%

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

      7. distribute-rgt-neg-in 46.1%

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

      8. *-commutative 46.1%

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

      9. distribute-rgt-neg-in 46.1%

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

      10. *-commutative 46.1%

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

      11. distribute-rgt-neg-in 46.1%

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

      12. *-commutative 46.1%

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

   9. Applied egg-rr 46.1%

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

   10. Taylor expanded in y around inf 66.9%

       \[\leadsto \frac{\color{blue}{-1 \cdot \left({y}^{2} \cdot \left({t}^{2} \cdot {x}^{2}\right)\right)}}{x - y \cdot \left(-x \cdot t\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 66.9%

          \[\leadsto \frac{\color{blue}{-{y}^{2} \cdot \left({t}^{2} \cdot {x}^{2}\right)}}{x - y \cdot \left(-x \cdot t\right)} \]

       2. unpow2 66.9%

          \[\leadsto \frac{-\color{blue}{\left(y \cdot y\right)} \cdot \left({t}^{2} \cdot {x}^{2}\right)}{x - y \cdot \left(-x \cdot t\right)} \]

       3. unpow2 66.9%

          \[\leadsto \frac{-\left(y \cdot y\right) \cdot \left(\color{blue}{\left(t \cdot t\right)} \cdot {x}^{2}\right)}{x - y \cdot \left(-x \cdot t\right)} \]

       4. unpow2 66.9%

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

   12. Simplified 66.9%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -260000000:\\ \;\;\;\;\frac{x \cdot x}{x + y \cdot \left(x \cdot t\right)}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{+70}:\\ \;\;\;\;\frac{x \cdot x}{x + y \cdot \left(x \cdot t\right)}\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+280}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot y\right) \cdot \left(\left(t \cdot t\right) \cdot \left(-x \cdot x\right)\right)}{x + y \cdot \left(x \cdot t\right)}\\ \end{array} \]

Alternative 9: 31.2% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{x + y \cdot \left(x \cdot t\right)}\\ \mathbf{if}\;b \leq -26000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+66} \lor \neg \left(b \leq 1.95 \cdot 10^{+277}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x x) (+ x (* y (* x t))))))
   (if (<= b -26000000.0)
     t_1
     (if (<= b 2.3e-13)
       (* x (- 1.0 (* y t)))
       (if (or (<= b 8e+66) (not (<= b 1.95e+277)))
         t_1
         (* x (- 1.0 (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * x) / (x + (y * (x * t)));
	double tmp;
	if (b <= -26000000.0) {
		tmp = t_1;
	} else if (b <= 2.3e-13) {
		tmp = x * (1.0 - (y * t));
	} else if ((b <= 8e+66) || !(b <= 1.95e+277)) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * x) / (x + (y * (x * t)))
    if (b <= (-26000000.0d0)) then
        tmp = t_1
    else if (b <= 2.3d-13) then
        tmp = x * (1.0d0 - (y * t))
    else if ((b <= 8d+66) .or. (.not. (b <= 1.95d+277))) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * x) / (x + (y * (x * t)));
	double tmp;
	if (b <= -26000000.0) {
		tmp = t_1;
	} else if (b <= 2.3e-13) {
		tmp = x * (1.0 - (y * t));
	} else if ((b <= 8e+66) || !(b <= 1.95e+277)) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * x) / (x + (y * (x * t)))
	tmp = 0
	if b <= -26000000.0:
		tmp = t_1
	elif b <= 2.3e-13:
		tmp = x * (1.0 - (y * t))
	elif (b <= 8e+66) or not (b <= 1.95e+277):
		tmp = t_1
	else:
		tmp = x * (1.0 - (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * x) / Float64(x + Float64(y * Float64(x * t))))
	tmp = 0.0
	if (b <= -26000000.0)
		tmp = t_1;
	elseif (b <= 2.3e-13)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif ((b <= 8e+66) || !(b <= 1.95e+277))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * x) / (x + (y * (x * t)));
	tmp = 0.0;
	if (b <= -26000000.0)
		tmp = t_1;
	elseif (b <= 2.3e-13)
		tmp = x * (1.0 - (y * t));
	elseif ((b <= 8e+66) || ~((b <= 1.95e+277)))
		tmp = t_1;
	else
		tmp = x * (1.0 - (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(x + N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -26000000.0], t$95$1, If[LessEqual[b, 2.3e-13], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 8e+66], N[Not[LessEqual[b, 1.95e+277]], $MachinePrecision]], t$95$1, N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6e7 or 2.29999999999999979e-13 < b < 7.99999999999999956e66 or 1.95000000000000002e277 < b

   1. Initial program 98.9%

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

   2. Taylor expanded in t around inf 42.2%

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

      1. mul-1-neg 42.2%

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

      2. distribute-rgt-neg-out 42.2%

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

   4. Simplified 42.2%

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

   5. Taylor expanded in y around 0 15.4%

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

      1. +-commutative 15.4%

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

      2. mul-1-neg 15.4%

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

      3. unsub-neg 15.4%

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

      4. *-commutative 15.4%

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

   7. Simplified 15.4%

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

      1. distribute-rgt-out-- 15.4%

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

      2. *-un-lft-identity 15.4%

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

      3. *-commutative 15.4%

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

      4. associate-*r* 16.4%

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

      5. sub-neg 16.4%

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

      6. flip-+ 23.6%

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

      7. distribute-rgt-neg-in 23.6%

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

      8. *-commutative 23.6%

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

      9. distribute-rgt-neg-in 23.6%

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

      10. *-commutative 23.6%

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

      11. distribute-rgt-neg-in 23.6%

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

      12. *-commutative 23.6%

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

   9. Applied egg-rr 23.6%

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

   10. Taylor expanded in y around 0 39.3%

       \[\leadsto \frac{\color{blue}{{x}^{2}}}{x - y \cdot \left(-x \cdot t\right)} \]
   11. Step-by-step derivation

       1. unpow2 39.3%

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

   12. Simplified 39.3%

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

   if -2.6e7 < b < 2.29999999999999979e-13

   1. Initial program 96.6%

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

   2. Taylor expanded in t around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-rgt-neg-out 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in y around 0 41.7%

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

      1. +-commutative 41.7%

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

      2. mul-1-neg 41.7%

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

      3. unsub-neg 41.7%

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

      4. *-commutative 41.7%

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

   7. Simplified 41.7%

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

   if 7.99999999999999956e66 < b < 1.95000000000000002e277

   1. Initial program 97.8%

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

   2. Taylor expanded in b around inf 77.1%

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

      1. associate-*r* 77.1%

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

      2. *-commutative 77.1%

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

      3. neg-mul-1 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in b around 0 33.7%

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

      1. mul-1-neg 33.7%

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

      2. unsub-neg 33.7%

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

      3. *-commutative 33.7%

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

   7. Simplified 33.7%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -26000000:\\ \;\;\;\;\frac{x \cdot x}{x + y \cdot \left(x \cdot t\right)}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+66} \lor \neg \left(b \leq 1.95 \cdot 10^{+277}\right):\\ \;\;\;\;\frac{x \cdot x}{x + y \cdot \left(x \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \]

Alternative 10: 29.2% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+246}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-199} \lor \neg \left(x \leq 1.22 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.5e+246)
   (* x (* t (- y)))
   (if (or (<= x -1.5e-199) (not (<= x 1.22e-63)))
     (* x (- 1.0 (* a b)))
     (* a (* x (- z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.5e+246) {
		tmp = x * (t * -y);
	} else if ((x <= -1.5e-199) || !(x <= 1.22e-63)) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6.5d+246)) then
        tmp = x * (t * -y)
    else if ((x <= (-1.5d-199)) .or. (.not. (x <= 1.22d-63))) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.5e+246) {
		tmp = x * (t * -y);
	} else if ((x <= -1.5e-199) || !(x <= 1.22e-63)) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.5e+246:
		tmp = x * (t * -y)
	elif (x <= -1.5e-199) or not (x <= 1.22e-63):
		tmp = x * (1.0 - (a * b))
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.5e+246)
		tmp = Float64(x * Float64(t * Float64(-y)));
	elseif ((x <= -1.5e-199) || !(x <= 1.22e-63))
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.5e+246)
		tmp = x * (t * -y);
	elseif ((x <= -1.5e-199) || ~((x <= 1.22e-63)))
		tmp = x * (1.0 - (a * b));
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.5e+246], N[(x * N[(t * (-y)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.5e-199], N[Not[LessEqual[x, 1.22e-63]], $MachinePrecision]], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.49999999999999977e246

   1. Initial program 91.7%

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

   2. Taylor expanded in t around inf 75.4%

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

      1. mul-1-neg 75.4%

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

      2. distribute-rgt-neg-out 75.4%

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

   4. Simplified 75.4%

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

   5. Taylor expanded in y around 0 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

   7. Simplified 50.8%

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

   8. Taylor expanded in t around inf 51.1%

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

      1. associate-*r* 51.1%

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

      2. *-commutative 51.1%

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

      3. *-commutative 51.1%

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

      4. neg-mul-1 51.1%

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

      5. distribute-rgt-neg-in 51.1%

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

      6. *-commutative 51.1%

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

      7. distribute-rgt-neg-out 51.1%

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

   10. Simplified 51.1%

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

   if -6.49999999999999977e246 < x < -1.49999999999999992e-199 or 1.2199999999999999e-63 < x

   1. Initial program 98.2%

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

   2. Taylor expanded in b around inf 58.2%

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

      1. associate-*r* 58.2%

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

      2. *-commutative 58.2%

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

      3. neg-mul-1 58.2%

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

   4. Simplified 58.2%

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

   5. Taylor expanded in b around 0 33.3%

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

      1. mul-1-neg 33.3%

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

      2. unsub-neg 33.3%

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

      3. *-commutative 33.3%

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

   7. Simplified 33.3%

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

   if -1.49999999999999992e-199 < x < 1.2199999999999999e-63

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 58.5%

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

      1. sub-neg 58.5%

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

      2. neg-mul-1 58.5%

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

      3. log1p-def 60.9%

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

      4. neg-mul-1 60.9%

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

   4. Simplified 60.9%

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

   5. Taylor expanded in z around 0 60.9%

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

      1. associate-*r* 60.9%

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

      2. associate-*r* 60.9%

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

      3. distribute-lft-out 60.9%

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

      4. neg-mul-1 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in a around 0 9.4%

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

      1. +-commutative 9.4%

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

      2. mul-1-neg 9.4%

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

      3. unsub-neg 9.4%

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

      4. *-commutative 9.4%

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

      5. +-commutative 9.4%

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

   10. Simplified 9.4%

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

   11. Taylor expanded in z around inf 35.2%

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

       1. mul-1-neg 35.2%

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

       2. distribute-rgt-neg-in 35.2%

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

       3. *-commutative 35.2%

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

   13. Simplified 35.2%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+246}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-199} \lor \neg \left(x \leq 1.22 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 11: 31.4% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -240000 \lor \neg \left(b \leq 5.2 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -240000.0) (not (<= b 5.2e-22)))
   (* x (- 1.0 (* a b)))
   (* x (- 1.0 (* y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -240000.0) || !(b <= 5.2e-22)) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (1.0 - (y * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-240000.0d0)) .or. (.not. (b <= 5.2d-22))) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (1.0d0 - (y * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -240000.0) || !(b <= 5.2e-22)) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (1.0 - (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -240000.0) or not (b <= 5.2e-22):
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (1.0 - (y * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -240000.0) || !(b <= 5.2e-22))
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -240000.0) || ~((b <= 5.2e-22)))
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (1.0 - (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -240000.0], N[Not[LessEqual[b, 5.2e-22]], $MachinePrecision]], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.4e5 or 5.2e-22 < b

   1. Initial program 98.6%

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

   2. Taylor expanded in b around inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. *-commutative 72.6%

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

      3. neg-mul-1 72.6%

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

   4. Simplified 72.6%

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

   5. Taylor expanded in b around 0 29.6%

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

      1. mul-1-neg 29.6%

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

      2. unsub-neg 29.6%

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

      3. *-commutative 29.6%

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

   7. Simplified 29.6%

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

   if -2.4e5 < b < 5.2e-22

   1. Initial program 96.6%

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

   2. Taylor expanded in t around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-rgt-neg-out 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in y around 0 41.2%

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

      1. +-commutative 41.2%

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

      2. mul-1-neg 41.2%

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

      3. unsub-neg 41.2%

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

      4. *-commutative 41.2%

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

   7. Simplified 41.2%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -240000 \lor \neg \left(b \leq 5.2 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \]

Alternative 12: 26.2% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+166} \lor \neg \left(y \leq 10^{-25}\right):\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.6e+166) (not (<= y 1e-25))) (* x (* t (- y))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.6e+166) || !(y <= 1e-25)) {
		tmp = x * (t * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.6d+166)) .or. (.not. (y <= 1d-25))) then
        tmp = x * (t * -y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.6e+166) || !(y <= 1e-25)) {
		tmp = x * (t * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.6e+166) or not (y <= 1e-25):
		tmp = x * (t * -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.6e+166) || !(y <= 1e-25))
		tmp = Float64(x * Float64(t * Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.6e+166) || ~((y <= 1e-25)))
		tmp = x * (t * -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.6e+166], N[Not[LessEqual[y, 1e-25]], $MachinePrecision]], N[(x * N[(t * (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999984e166 or 1.00000000000000004e-25 < y

   1. Initial program 97.3%

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

   2. Taylor expanded in t around inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. distribute-rgt-neg-out 64.5%

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

   4. Simplified 64.5%

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

   5. Taylor expanded in y around 0 26.9%

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

      1. +-commutative 26.9%

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

      2. mul-1-neg 26.9%

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

      3. unsub-neg 26.9%

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

      4. *-commutative 26.9%

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

   7. Simplified 26.9%

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

   8. Taylor expanded in t around inf 27.6%

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

      1. associate-*r* 28.5%

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

      2. *-commutative 28.5%

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

      3. *-commutative 28.5%

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

      4. neg-mul-1 28.5%

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

      5. distribute-rgt-neg-in 28.5%

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

      6. *-commutative 28.5%

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

      7. distribute-rgt-neg-out 28.5%

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

   10. Simplified 28.5%

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

   if -1.59999999999999984e166 < y < 1.00000000000000004e-25

   1. Initial program 98.0%

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

   2. Taylor expanded in b around inf 72.8%

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

      1. associate-*r* 72.8%

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

      2. *-commutative 72.8%

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

      3. neg-mul-1 72.8%

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

   4. Simplified 72.8%

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

   5. Taylor expanded in b around 0 26.5%

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

4. Final simplification 27.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+166} \lor \neg \left(y \leq 10^{-25}\right):\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 26.2% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.9e+15)
   (* a (* x (- z)))
   (if (<= y 6.2e-18) x (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.9e+15) {
		tmp = a * (x * -z);
	} else if (y <= 6.2e-18) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.9d+15)) then
        tmp = a * (x * -z)
    else if (y <= 6.2d-18) then
        tmp = x
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.9e+15) {
		tmp = a * (x * -z);
	} else if (y <= 6.2e-18) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.9e+15:
		tmp = a * (x * -z)
	elif y <= 6.2e-18:
		tmp = x
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.9e+15)
		tmp = Float64(a * Float64(x * Float64(-z)));
	elseif (y <= 6.2e-18)
		tmp = x;
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.9e+15)
		tmp = a * (x * -z);
	elseif (y <= 6.2e-18)
		tmp = x;
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.9e+15], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-18], x, N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9e15

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 32.2%

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

      1. sub-neg 32.2%

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

      2. neg-mul-1 32.2%

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

      3. log1p-def 29.1%

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

      4. neg-mul-1 29.1%

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

   4. Simplified 29.1%

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

   5. Taylor expanded in z around 0 29.1%

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

      1. associate-*r* 29.1%

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

      2. associate-*r* 29.1%

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

      3. distribute-lft-out 29.1%

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

      4. neg-mul-1 29.1%

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

   7. Simplified 29.1%

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

   8. Taylor expanded in a around 0 8.8%

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

      1. +-commutative 8.8%

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

      2. mul-1-neg 8.8%

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

      3. unsub-neg 8.8%

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

      4. *-commutative 8.8%

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

      5. +-commutative 8.8%

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

   10. Simplified 8.8%

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

   11. Taylor expanded in z around inf 12.8%

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

       1. mul-1-neg 12.8%

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

       2. distribute-rgt-neg-in 12.8%

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

       3. *-commutative 12.8%

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

   13. Simplified 12.8%

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

   if -3.9e15 < y < 6.20000000000000014e-18

   1. Initial program 97.6%

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

   2. Taylor expanded in b around inf 79.4%

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

      1. associate-*r* 79.4%

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

      2. *-commutative 79.4%

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

      3. neg-mul-1 79.4%

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

   4. Simplified 79.4%

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

   5. Taylor expanded in b around 0 31.0%

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

   if 6.20000000000000014e-18 < y

   1. Initial program 97.2%

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

   2. Taylor expanded in b around inf 41.5%

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

      1. associate-*r* 41.5%

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

      2. *-commutative 41.5%

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

      3. neg-mul-1 41.5%

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

   4. Simplified 41.5%

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

   5. Taylor expanded in b around 0 16.9%

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

      1. mul-1-neg 16.9%

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

      2. unsub-neg 16.9%

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

      3. *-commutative 16.9%

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

   7. Simplified 16.9%

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

   8. Taylor expanded in b around inf 27.8%

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

      1. mul-1-neg 27.8%

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

      2. distribute-rgt-neg-in 27.8%

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

   10. Simplified 27.8%

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

4. Final simplification 25.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 14: 26.9% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.85 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.85e-16)
   (* y (* x (- t)))
   (if (<= y 2.3e-25) x (* x (* t (- y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.85e-16) {
		tmp = y * (x * -t);
	} else if (y <= 2.3e-25) {
		tmp = x;
	} else {
		tmp = x * (t * -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.85d-16)) then
        tmp = y * (x * -t)
    else if (y <= 2.3d-25) then
        tmp = x
    else
        tmp = x * (t * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.85e-16) {
		tmp = y * (x * -t);
	} else if (y <= 2.3e-25) {
		tmp = x;
	} else {
		tmp = x * (t * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.85e-16:
		tmp = y * (x * -t)
	elif y <= 2.3e-25:
		tmp = x
	else:
		tmp = x * (t * -y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.85e-16)
		tmp = Float64(y * Float64(x * Float64(-t)));
	elseif (y <= 2.3e-25)
		tmp = x;
	else
		tmp = Float64(x * Float64(t * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.85e-16)
		tmp = y * (x * -t);
	elseif (y <= 2.3e-25)
		tmp = x;
	else
		tmp = x * (t * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.85e-16], N[(y * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-25], x, N[(x * N[(t * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.84999999999999994e-16

   1. Initial program 98.6%

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

   2. Taylor expanded in t around inf 46.4%

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

      1. mul-1-neg 46.4%

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

      2. distribute-rgt-neg-out 46.4%

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

   4. Simplified 46.4%

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

   5. Taylor expanded in y around 0 16.9%

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

      1. +-commutative 16.9%

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

      2. mul-1-neg 16.9%

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

      3. unsub-neg 16.9%

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

      4. *-commutative 16.9%

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

   7. Simplified 16.9%

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

   8. Taylor expanded in t around inf 17.7%

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

      1. associate-*r* 17.7%

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

      2. neg-mul-1 17.7%

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

      3. *-commutative 17.7%

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

      4. *-commutative 17.7%

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

   10. Simplified 17.7%

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

   if -3.84999999999999994e-16 < y < 2.2999999999999999e-25

   1. Initial program 97.4%

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

   2. Taylor expanded in b around inf 83.7%

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

      1. associate-*r* 83.7%

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

      2. *-commutative 83.7%

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

      3. neg-mul-1 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in b around 0 33.1%

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

   if 2.2999999999999999e-25 < y

   1. Initial program 97.3%

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

   2. Taylor expanded in t around inf 67.1%

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

      1. mul-1-neg 67.1%

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

      2. distribute-rgt-neg-out 67.1%

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

   4. Simplified 67.1%

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

   5. Taylor expanded in y around 0 25.6%

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

      1. +-commutative 25.6%

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

      2. mul-1-neg 25.6%

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

      3. unsub-neg 25.6%

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

      4. *-commutative 25.6%

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

   7. Simplified 25.6%

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

   8. Taylor expanded in t around inf 26.7%

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

      1. associate-*r* 28.1%

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

      2. *-commutative 28.1%

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

      3. *-commutative 28.1%

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

      4. neg-mul-1 28.1%

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

      5. distribute-rgt-neg-in 28.1%

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

      6. *-commutative 28.1%

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

      7. distribute-rgt-neg-out 28.1%

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

   10. Simplified 28.1%

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

4. Final simplification 27.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.85 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 15: 24.2% accurate, 39.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 2.5e-19) x (* a (* x (- b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.5e-19) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 2.5d-19) then
        tmp = x
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.5e-19) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 2.5e-19:
		tmp = x
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 2.5e-19)
		tmp = x;
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 2.5e-19)
		tmp = x;
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 2.5e-19], x, N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5000000000000002e-19

   1. Initial program 97.9%

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

   2. Taylor expanded in b around inf 62.9%

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

      1. associate-*r* 62.9%

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

      2. *-commutative 62.9%

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

      3. neg-mul-1 62.9%

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

   4. Simplified 62.9%

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

   5. Taylor expanded in b around 0 21.7%

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

   if 2.5000000000000002e-19 < y

   1. Initial program 97.2%

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

   2. Taylor expanded in b around inf 41.5%

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

      1. associate-*r* 41.5%

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

      2. *-commutative 41.5%

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

      3. neg-mul-1 41.5%

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

   4. Simplified 41.5%

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

   5. Taylor expanded in b around 0 16.9%

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

      1. mul-1-neg 16.9%

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

      2. unsub-neg 16.9%

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

      3. *-commutative 16.9%

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

   7. Simplified 16.9%

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

   8. Taylor expanded in b around inf 27.8%

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

      1. mul-1-neg 27.8%

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

      2. distribute-rgt-neg-in 27.8%

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

   10. Simplified 27.8%

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

4. Final simplification 23.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 16: 20.3% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.95 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= a 1.95e+80) x (* x (* y t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.95e+80) {
		tmp = x;
	} else {
		tmp = x * (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.95d+80) then
        tmp = x
    else
        tmp = x * (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.95e+80) {
		tmp = x;
	} else {
		tmp = x * (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.95e+80:
		tmp = x
	else:
		tmp = x * (y * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.95e+80)
		tmp = x;
	else
		tmp = Float64(x * Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.95e+80)
		tmp = x;
	else
		tmp = x * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.95e+80], x, N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.94999999999999999e80

   1. Initial program 99.0%

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

   2. Taylor expanded in b around inf 51.9%

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

      1. associate-*r* 51.9%

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

      2. *-commutative 51.9%

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

      3. neg-mul-1 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in b around 0 19.1%

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

   if 1.94999999999999999e80 < a

   1. Initial program 91.4%

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

   2. Taylor expanded in t around inf 37.6%

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

      1. mul-1-neg 37.6%

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

      2. distribute-rgt-neg-out 37.6%

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

   4. Simplified 37.6%

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

   5. Taylor expanded in y around 0 11.9%

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

      1. +-commutative 11.9%

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

      2. mul-1-neg 11.9%

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

      3. unsub-neg 11.9%

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

      4. *-commutative 11.9%

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

   7. Simplified 11.9%

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

   8. Taylor expanded in t around inf 24.9%

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

      1. associate-*r* 24.9%

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

      2. neg-mul-1 24.9%

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

      3. *-commutative 24.9%

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

      4. *-commutative 24.9%

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

   10. Simplified 24.9%

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

       1. *-commutative 24.9%

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

       2. add-sqr-sqrt 14.7%

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

       3. sqrt-unprod 33.6%

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

       4. sqr-neg 33.6%

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

       5. sqrt-unprod 22.1%

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

       6. add-sqr-sqrt 22.7%

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

       7. add-sqr-sqrt 7.7%

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

       8. sqrt-unprod 28.3%

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

       9. sqr-neg 28.3%

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

       10. sqrt-unprod 17.5%

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

       11. add-sqr-sqrt 24.9%

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

       12. expm1-log1p-u 22.0%

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

       13. expm1-udef 25.4%

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

   12. Applied egg-rr 23.7%

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

       1. expm1-def 18.3%

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

       2. expm1-log1p 20.6%

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

       3. *-commutative 20.6%

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

   14. Simplified 20.6%

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

4. Final simplification 19.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.95 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 17: 18.9% 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 97.7%

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

2. Taylor expanded in b around inf 56.9%

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

   1. associate-*r* 56.9%

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

   2. *-commutative 56.9%

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

   3. neg-mul-1 56.9%

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

4. Simplified 56.9%

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

5. Taylor expanded in b around 0 16.8%

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

6. Final simplification 16.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023230 
(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))))))