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

Percentage Accurate: 96.3% → 98.9%

Time: 14.1s

Alternatives: 16

Speedup: 1.5×

• 41.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.3% 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: 98.9% accurate, 1.5× speedup

Math

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

FPCore

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

Python

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) - (a * (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[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Taylor expanded in z around 0 100.0%

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

   1. associate-*r* 100.0%

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

   2. associate-*r* 100.0%

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

   3. distribute-lft-out 100.0%

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

   4. mul-1-neg 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 87.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-5} \lor \neg \left(y \leq 1.5 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.6e-5) (not (<= y 1.5e-19)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (- b) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.6e-5) || !(y <= 1.5e-19)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * (-b - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.6d-5)) .or. (.not. (y <= 1.5d-19))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((a * (-b - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.6e-5) || !(y <= 1.5e-19)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * (-b - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.6e-5) or not (y <= 1.5e-19):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * (-b - z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.6e-5) || !(y <= 1.5e-19))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-b) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.6e-5) || ~((y <= 1.5e-19)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((a * (-b - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.6e-5], N[Not[LessEqual[y, 1.5e-19]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[((-b) - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999984e-5 or 1.49999999999999996e-19 < y

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 90.8%

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

   if -2.59999999999999984e-5 < y < 1.49999999999999996e-19

   1. Initial program 95.5%

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

      1. fma-define 95.5%

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

      2. sub-neg 95.5%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 81.1%

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

   6. Taylor expanded in z around 0 87.1%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. mul-1-neg 100.0%

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

   8. Simplified 87.1%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-5} \lor \neg \left(y \leq 1.5 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -50 \lor \neg \left(y \leq 130000000000\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -50.0) (not (<= y 130000000000.0)))
   (* x (pow z y))
   (* x (exp (* a (- (- b) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -50.0) || !(y <= 130000000000.0)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp((a * (-b - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-50.0d0)) .or. (.not. (y <= 130000000000.0d0))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp((a * (-b - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -50.0) || !(y <= 130000000000.0)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((a * (-b - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -50.0) or not (y <= 130000000000.0):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((a * (-b - z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -50.0) || !(y <= 130000000000.0))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-b) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -50.0) || ~((y <= 130000000000.0)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((a * (-b - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -50.0], N[Not[LessEqual[y, 130000000000.0]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[((-b) - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -50 or 1.3e11 < y

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 91.1%

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

   6. Taylor expanded in t around 0 76.6%

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

   if -50 < y < 1.3e11

   1. Initial program 95.7%

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

      1. fma-define 95.7%

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

      2. sub-neg 95.7%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 79.6%

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

   6. Taylor expanded in z around 0 85.3%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. mul-1-neg 100.0%

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

   8. Simplified 85.3%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -50 \lor \neg \left(y \leq 130000000000\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.13 \lor \neg \left(y \leq 20000000000\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.13) (not (<= y 20000000000.0)))
   (* 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 <= -0.13) || !(y <= 20000000000.0)) {
		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 <= (-0.13d0)) .or. (.not. (y <= 20000000000.0d0))) 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 <= -0.13) || !(y <= 20000000000.0)) {
		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 <= -0.13) or not (y <= 20000000000.0):
		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 <= -0.13) || !(y <= 20000000000.0))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -0.13) || ~((y <= 20000000000.0)))
		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, -0.13], N[Not[LessEqual[y, 20000000000.0]], $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 < -0.13 or 2e10 < y

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 91.1%

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

   6. Taylor expanded in t around 0 76.6%

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

   if -0.13 < y < 2e10

   1. Initial program 95.7%

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

      1. fma-define 95.7%

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

      2. sub-neg 95.7%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 79.6%

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

   6. Taylor expanded in z around 0 79.6%

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

      1. associate-*r* 79.6%

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

      2. mul-1-neg 79.6%

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

   8. Simplified 79.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.13 \lor \neg \left(y \leq 20000000000\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-13} \lor \neg \left(y \leq 1.5 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.8e-13) (not (<= y 1.5e-31)))
   (* x (pow z y))
   (* x (- 1.0 (* a (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.8e-13) || !(y <= 1.5e-31)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * (1.0 - (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 <= (-8.8d-13)) .or. (.not. (y <= 1.5d-31))) then
        tmp = x * (z ** y)
    else
        tmp = x * (1.0d0 - (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 <= -8.8e-13) || !(y <= 1.5e-31)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * (1.0 - (a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.8e-13) or not (y <= 1.5e-31):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * (1.0 - (a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.8e-13) || !(y <= 1.5e-31))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * Float64(1.0 - Float64(a * Float64(z + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.8e-13) || ~((y <= 1.5e-31)))
		tmp = x * (z ^ y);
	else
		tmp = x * (1.0 - (a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.8e-13], N[Not[LessEqual[y, 1.5e-31]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.79999999999999986e-13 or 1.49999999999999991e-31 < y

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 88.9%

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

   6. Taylor expanded in t around 0 72.7%

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

   if -8.79999999999999986e-13 < y < 1.49999999999999991e-31

   1. Initial program 95.4%

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

      1. fma-define 95.4%

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

      2. sub-neg 95.4%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 80.3%

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

   6. Taylor expanded in z around 0 86.5%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. mul-1-neg 100.0%

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

   8. Simplified 86.5%

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

   9. Taylor expanded in a around 0 47.2%

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

       1. mul-1-neg 47.2%

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

       2. unsub-neg 47.2%

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

   11. Simplified 47.2%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-13} \lor \neg \left(y \leq 1.5 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 22.9% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-6}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-88}:\\ \;\;\;\;x + x \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+219}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.9e-6)
   (* a (* x (- b)))
   (if (<= a 4.9e-88)
     (+ x (* x (* a b)))
     (if (<= a 7.6e+219) (* b (* x (- a))) (* (* x t) (- y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.9e-6) {
		tmp = a * (x * -b);
	} else if (a <= 4.9e-88) {
		tmp = x + (x * (a * b));
	} else if (a <= 7.6e+219) {
		tmp = b * (x * -a);
	} 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 (a <= (-1.9d-6)) then
        tmp = a * (x * -b)
    else if (a <= 4.9d-88) then
        tmp = x + (x * (a * b))
    else if (a <= 7.6d+219) then
        tmp = b * (x * -a)
    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 (a <= -1.9e-6) {
		tmp = a * (x * -b);
	} else if (a <= 4.9e-88) {
		tmp = x + (x * (a * b));
	} else if (a <= 7.6e+219) {
		tmp = b * (x * -a);
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.9e-6:
		tmp = a * (x * -b)
	elif a <= 4.9e-88:
		tmp = x + (x * (a * b))
	elif a <= 7.6e+219:
		tmp = b * (x * -a)
	else:
		tmp = (x * t) * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.9e-6)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (a <= 4.9e-88)
		tmp = Float64(x + Float64(x * Float64(a * b)));
	elseif (a <= 7.6e+219)
		tmp = Float64(b * Float64(x * Float64(-a)));
	else
		tmp = Float64(Float64(x * t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.9e-6)
		tmp = a * (x * -b);
	elseif (a <= 4.9e-88)
		tmp = x + (x * (a * b));
	elseif (a <= 7.6e+219)
		tmp = b * (x * -a);
	else
		tmp = (x * t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.9e-6], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e-88], N[(x + N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e+219], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.9e-6

   1. Initial program 94.5%

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

      1. fma-define 94.5%

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

      2. sub-neg 94.5%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 66.4%

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

   6. Taylor expanded in z around 0 66.4%

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

      1. associate-*r* 66.4%

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

      2. mul-1-neg 66.4%

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

   8. Simplified 66.4%

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

   9. Taylor expanded in a around 0 24.3%

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

       1. mul-1-neg 24.3%

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

       2. unsub-neg 24.3%

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

       3. *-commutative 24.3%

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

   11. Simplified 24.3%

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

   12. Taylor expanded in a around inf 28.3%

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

   if -1.9e-6 < a < 4.90000000000000028e-88

   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. Step-by-step derivation

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 51.3%

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

   6. Taylor expanded in z around 0 51.3%

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

      1. associate-*r* 51.3%

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

      2. mul-1-neg 51.3%

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

   8. Simplified 51.3%

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

   9. Taylor expanded in a around 0 36.9%

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

       1. mul-1-neg 36.9%

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

       2. unsub-neg 36.9%

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

       3. *-commutative 36.9%

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

   11. Simplified 36.9%

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

       1. cancel-sign-sub-inv 36.9%

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

       2. add-sqr-sqrt 17.9%

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

       3. sqrt-unprod 35.0%

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

       4. sqr-neg 35.0%

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

       5. sqrt-unprod 17.1%

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

       6. add-sqr-sqrt 35.7%

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

       7. +-commutative 35.7%

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

       8. *-commutative 35.7%

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

       9. associate-*l* 35.8%

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

       10. *-commutative 35.8%

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

   13. Applied egg-rr 35.8%

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

   if 4.90000000000000028e-88 < a < 7.59999999999999992e219

   1. Initial program 98.5%

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

      1. fma-define 98.5%

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

      2. sub-neg 98.5%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 57.8%

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

   6. Taylor expanded in z around 0 59.4%

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

      1. associate-*r* 59.4%

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

      2. mul-1-neg 59.4%

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

   8. Simplified 59.4%

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

   9. Taylor expanded in a around 0 23.5%

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

       1. mul-1-neg 23.5%

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

       2. unsub-neg 23.5%

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

       3. *-commutative 23.5%

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

   11. Simplified 23.5%

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

   12. Taylor expanded in a around inf 26.7%

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

       1. associate-*r* 29.6%

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

       2. associate-*r* 29.6%

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

       3. *-commutative 29.6%

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

       4. associate-*r* 29.6%

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

       5. associate-*r* 32.7%

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

       6. mul-1-neg 32.7%

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

   14. Simplified 32.7%

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

   if 7.59999999999999992e219 < a

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 31.5%

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

      1. associate-*r* 31.5%

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

      2. neg-mul-1 31.5%

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

   8. Simplified 31.5%

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

   9. Taylor expanded in t around 0 14.7%

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

       1. mul-1-neg 14.7%

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

       2. unsub-neg 14.7%

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

       3. associate-*r* 14.7%

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

       4. *-commutative 14.7%

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

       5. *-commutative 14.7%

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

   11. Simplified 14.7%

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

   12. Taylor expanded in y around inf 31.8%

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

       1. mul-1-neg 31.8%

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

       2. associate-*r* 37.2%

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

       3. *-commutative 37.2%

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

   14. Simplified 37.2%

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

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-6}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-88}:\\ \;\;\;\;x + x \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+219}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 23.2% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-6}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-88}:\\ \;\;\;\;x + t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+221}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.9e-6)
   (* a (* x (- b)))
   (if (<= a 6.5e-88)
     (+ x (* t (* x y)))
     (if (<= a 1.95e+221) (* b (* x (- a))) (* (* x t) (- y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.9e-6) {
		tmp = a * (x * -b);
	} else if (a <= 6.5e-88) {
		tmp = x + (t * (x * y));
	} else if (a <= 1.95e+221) {
		tmp = b * (x * -a);
	} 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 (a <= (-1.9d-6)) then
        tmp = a * (x * -b)
    else if (a <= 6.5d-88) then
        tmp = x + (t * (x * y))
    else if (a <= 1.95d+221) then
        tmp = b * (x * -a)
    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 (a <= -1.9e-6) {
		tmp = a * (x * -b);
	} else if (a <= 6.5e-88) {
		tmp = x + (t * (x * y));
	} else if (a <= 1.95e+221) {
		tmp = b * (x * -a);
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.9e-6:
		tmp = a * (x * -b)
	elif a <= 6.5e-88:
		tmp = x + (t * (x * y))
	elif a <= 1.95e+221:
		tmp = b * (x * -a)
	else:
		tmp = (x * t) * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.9e-6)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (a <= 6.5e-88)
		tmp = Float64(x + Float64(t * Float64(x * y)));
	elseif (a <= 1.95e+221)
		tmp = Float64(b * Float64(x * Float64(-a)));
	else
		tmp = Float64(Float64(x * t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.9e-6)
		tmp = a * (x * -b);
	elseif (a <= 6.5e-88)
		tmp = x + (t * (x * y));
	elseif (a <= 1.95e+221)
		tmp = b * (x * -a);
	else
		tmp = (x * t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.9e-6], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-88], N[(x + N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e+221], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.9e-6

   1. Initial program 94.5%

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

      1. fma-define 94.5%

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

      2. sub-neg 94.5%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 66.4%

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

   6. Taylor expanded in z around 0 66.4%

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

      1. associate-*r* 66.4%

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

      2. mul-1-neg 66.4%

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

   8. Simplified 66.4%

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

   9. Taylor expanded in a around 0 24.3%

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

       1. mul-1-neg 24.3%

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

       2. unsub-neg 24.3%

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

       3. *-commutative 24.3%

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

   11. Simplified 24.3%

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

   12. Taylor expanded in a around inf 28.3%

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

   if -1.9e-6 < a < 6.50000000000000006e-88

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

   9. Taylor expanded in t around 0 40.4%

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

       1. associate-*r* 40.4%

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

       2. mul-1-neg 40.4%

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

   11. Simplified 40.4%

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

       1. neg-sub0 40.4%

          \[\leadsto x + \color{blue}{\left(0 - t\right)} \cdot \left(x \cdot y\right) \]

       2. sub-neg 40.4%

          \[\leadsto x + \color{blue}{\left(0 + \left(-t\right)\right)} \cdot \left(x \cdot y\right) \]

       3. add-sqr-sqrt 19.0%

          \[\leadsto x + \left(0 + \color{blue}{\sqrt{-t} \cdot \sqrt{-t}}\right) \cdot \left(x \cdot y\right) \]

       4. sqrt-unprod 36.1%

          \[\leadsto x + \left(0 + \color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}\right) \cdot \left(x \cdot y\right) \]

       5. sqr-neg 36.1%

          \[\leadsto x + \left(0 + \sqrt{\color{blue}{t \cdot t}}\right) \cdot \left(x \cdot y\right) \]

       6. sqrt-unprod 17.4%

          \[\leadsto x + \left(0 + \color{blue}{\sqrt{t} \cdot \sqrt{t}}\right) \cdot \left(x \cdot y\right) \]

       7. add-sqr-sqrt 35.4%

          \[\leadsto x + \left(0 + \color{blue}{t}\right) \cdot \left(x \cdot y\right) \]

   13. Applied egg-rr 35.4%

       \[\leadsto x + \color{blue}{\left(0 + t\right)} \cdot \left(x \cdot y\right) \]
   14. Step-by-step derivation

       1. +-lft-identity 35.4%

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

   15. Simplified 35.4%

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

   if 6.50000000000000006e-88 < a < 1.95e221

   1. Initial program 98.5%

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

      1. fma-define 98.5%

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

      2. sub-neg 98.5%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 57.8%

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

   6. Taylor expanded in z around 0 59.4%

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

      1. associate-*r* 59.4%

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

      2. mul-1-neg 59.4%

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

   8. Simplified 59.4%

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

   9. Taylor expanded in a around 0 23.5%

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

       1. mul-1-neg 23.5%

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

       2. unsub-neg 23.5%

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

       3. *-commutative 23.5%

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

   11. Simplified 23.5%

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

   12. Taylor expanded in a around inf 26.7%

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

       1. associate-*r* 29.6%

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

       2. associate-*r* 29.6%

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

       3. *-commutative 29.6%

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

       4. associate-*r* 29.6%

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

       5. associate-*r* 32.7%

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

       6. mul-1-neg 32.7%

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

   14. Simplified 32.7%

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

   if 1.95e221 < a

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 31.5%

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

      1. associate-*r* 31.5%

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

      2. neg-mul-1 31.5%

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

   8. Simplified 31.5%

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

   9. Taylor expanded in t around 0 14.7%

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

       1. mul-1-neg 14.7%

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

       2. unsub-neg 14.7%

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

       3. associate-*r* 14.7%

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

       4. *-commutative 14.7%

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

       5. *-commutative 14.7%

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

   11. Simplified 14.7%

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

   12. Taylor expanded in y around inf 31.8%

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

       1. mul-1-neg 31.8%

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

       2. associate-*r* 37.2%

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

       3. *-commutative 37.2%

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

   14. Simplified 37.2%

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

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-6}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-88}:\\ \;\;\;\;x + t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+221}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 23.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-7}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+215}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.2e-7)
   (* a (* x (- b)))
   (if (<= a 6e-88) x (if (<= a 3e+215) (* b (* x (- a))) (* (* x t) (- y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.2e-7) {
		tmp = a * (x * -b);
	} else if (a <= 6e-88) {
		tmp = x;
	} else if (a <= 3e+215) {
		tmp = b * (x * -a);
	} 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 (a <= (-1.2d-7)) then
        tmp = a * (x * -b)
    else if (a <= 6d-88) then
        tmp = x
    else if (a <= 3d+215) then
        tmp = b * (x * -a)
    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 (a <= -1.2e-7) {
		tmp = a * (x * -b);
	} else if (a <= 6e-88) {
		tmp = x;
	} else if (a <= 3e+215) {
		tmp = b * (x * -a);
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.2e-7:
		tmp = a * (x * -b)
	elif a <= 6e-88:
		tmp = x
	elif a <= 3e+215:
		tmp = b * (x * -a)
	else:
		tmp = (x * t) * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.2e-7)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (a <= 6e-88)
		tmp = x;
	elseif (a <= 3e+215)
		tmp = Float64(b * Float64(x * Float64(-a)));
	else
		tmp = Float64(Float64(x * t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.2e-7)
		tmp = a * (x * -b);
	elseif (a <= 6e-88)
		tmp = x;
	elseif (a <= 3e+215)
		tmp = b * (x * -a);
	else
		tmp = (x * t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.2e-7], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-88], x, If[LessEqual[a, 3e+215], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.19999999999999989e-7

   1. Initial program 94.5%

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

      1. fma-define 94.5%

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

      2. sub-neg 94.5%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 66.4%

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

   6. Taylor expanded in z around 0 66.4%

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

      1. associate-*r* 66.4%

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

      2. mul-1-neg 66.4%

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

   8. Simplified 66.4%

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

   9. Taylor expanded in a around 0 24.3%

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

       1. mul-1-neg 24.3%

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

       2. unsub-neg 24.3%

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

       3. *-commutative 24.3%

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

   11. Simplified 24.3%

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

   12. Taylor expanded in a around inf 28.3%

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

   if -1.19999999999999989e-7 < a < 5.9999999999999999e-88

   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. Step-by-step derivation

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 51.3%

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

   6. Taylor expanded in a around 0 34.4%

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

   if 5.9999999999999999e-88 < a < 2.9999999999999999e215

   1. Initial program 98.5%

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

      1. fma-define 98.5%

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

      2. sub-neg 98.5%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 57.8%

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

   6. Taylor expanded in z around 0 59.4%

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

      1. associate-*r* 59.4%

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

      2. mul-1-neg 59.4%

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

   8. Simplified 59.4%

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

   9. Taylor expanded in a around 0 23.5%

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

       1. mul-1-neg 23.5%

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

       2. unsub-neg 23.5%

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

       3. *-commutative 23.5%

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

   11. Simplified 23.5%

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

   12. Taylor expanded in a around inf 26.7%

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

       1. associate-*r* 29.6%

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

       2. associate-*r* 29.6%

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

       3. *-commutative 29.6%

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

       4. associate-*r* 29.6%

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

       5. associate-*r* 32.7%

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

       6. mul-1-neg 32.7%

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

   14. Simplified 32.7%

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

   if 2.9999999999999999e215 < a

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 31.5%

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

      1. associate-*r* 31.5%

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

      2. neg-mul-1 31.5%

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

   8. Simplified 31.5%

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

   9. Taylor expanded in t around 0 14.7%

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

       1. mul-1-neg 14.7%

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

       2. unsub-neg 14.7%

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

       3. associate-*r* 14.7%

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

       4. *-commutative 14.7%

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

       5. *-commutative 14.7%

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

   11. Simplified 14.7%

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

   12. Taylor expanded in y around inf 31.8%

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

       1. mul-1-neg 31.8%

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

       2. associate-*r* 37.2%

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

       3. *-commutative 37.2%

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

   14. Simplified 37.2%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-7}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+215}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 23.6% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+221}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.6e-6)
   (* x (* a (- b)))
   (if (<= a 4.4e-88)
     x
     (if (<= a 1.4e+221) (* b (* x (- a))) (* (* x t) (- y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.6e-6) {
		tmp = x * (a * -b);
	} else if (a <= 4.4e-88) {
		tmp = x;
	} else if (a <= 1.4e+221) {
		tmp = b * (x * -a);
	} 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 (a <= (-1.6d-6)) then
        tmp = x * (a * -b)
    else if (a <= 4.4d-88) then
        tmp = x
    else if (a <= 1.4d+221) then
        tmp = b * (x * -a)
    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 (a <= -1.6e-6) {
		tmp = x * (a * -b);
	} else if (a <= 4.4e-88) {
		tmp = x;
	} else if (a <= 1.4e+221) {
		tmp = b * (x * -a);
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.6e-6:
		tmp = x * (a * -b)
	elif a <= 4.4e-88:
		tmp = x
	elif a <= 1.4e+221:
		tmp = b * (x * -a)
	else:
		tmp = (x * t) * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.6e-6)
		tmp = Float64(x * Float64(a * Float64(-b)));
	elseif (a <= 4.4e-88)
		tmp = x;
	elseif (a <= 1.4e+221)
		tmp = Float64(b * Float64(x * Float64(-a)));
	else
		tmp = Float64(Float64(x * t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.6e-6)
		tmp = x * (a * -b);
	elseif (a <= 4.4e-88)
		tmp = x;
	elseif (a <= 1.4e+221)
		tmp = b * (x * -a);
	else
		tmp = (x * t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.6e-6], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e-88], x, If[LessEqual[a, 1.4e+221], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.5999999999999999e-6

   1. Initial program 94.5%

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

      1. fma-define 94.5%

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

      2. sub-neg 94.5%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 66.4%

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

   6. Taylor expanded in z around 0 66.4%

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

      1. associate-*r* 66.4%

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

      2. mul-1-neg 66.4%

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

   8. Simplified 66.4%

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

   9. Taylor expanded in a around 0 24.3%

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

       1. mul-1-neg 24.3%

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

       2. unsub-neg 24.3%

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

       3. *-commutative 24.3%

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

   11. Simplified 24.3%

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

   12. Taylor expanded in a around inf 28.3%

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

       1. associate-*r* 25.6%

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

       2. associate-*r* 25.6%

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

       3. *-commutative 25.6%

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

       4. associate-*r* 25.6%

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

       5. mul-1-neg 25.6%

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

   14. Simplified 25.6%

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

   if -1.5999999999999999e-6 < a < 4.4000000000000001e-88

   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. Step-by-step derivation

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 51.3%

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

   6. Taylor expanded in a around 0 34.4%

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

   if 4.4000000000000001e-88 < a < 1.39999999999999994e221

   1. Initial program 98.5%

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

      1. fma-define 98.5%

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

      2. sub-neg 98.5%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 57.8%

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

   6. Taylor expanded in z around 0 59.4%

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

      1. associate-*r* 59.4%

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

      2. mul-1-neg 59.4%

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

   8. Simplified 59.4%

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

   9. Taylor expanded in a around 0 23.5%

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

       1. mul-1-neg 23.5%

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

       2. unsub-neg 23.5%

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

       3. *-commutative 23.5%

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

   11. Simplified 23.5%

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

   12. Taylor expanded in a around inf 26.7%

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

       1. associate-*r* 29.6%

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

       2. associate-*r* 29.6%

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

       3. *-commutative 29.6%

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

       4. associate-*r* 29.6%

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

       5. associate-*r* 32.7%

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

       6. mul-1-neg 32.7%

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

   14. Simplified 32.7%

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

   if 1.39999999999999994e221 < a

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 31.5%

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

      1. associate-*r* 31.5%

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

      2. neg-mul-1 31.5%

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

   8. Simplified 31.5%

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

   9. Taylor expanded in t around 0 14.7%

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

       1. mul-1-neg 14.7%

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

       2. unsub-neg 14.7%

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

       3. associate-*r* 14.7%

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

       4. *-commutative 14.7%

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

       5. *-commutative 14.7%

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

   11. Simplified 14.7%

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

   12. Taylor expanded in y around inf 31.8%

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

       1. mul-1-neg 31.8%

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

       2. associate-*r* 37.2%

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

       3. *-commutative 37.2%

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

   14. Simplified 37.2%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+221}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 31.5% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-9}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.4e+109)
   (* b (* x (- a)))
   (if (<= y 6.2e-9) (- x (* x (* a b))) (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.4e+109) {
		tmp = b * (x * -a);
	} else if (y <= 6.2e-9) {
		tmp = x - (x * (a * b));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.4d+109)) then
        tmp = b * (x * -a)
    else if (y <= 6.2d-9) then
        tmp = x - (x * (a * b))
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.4e+109) {
		tmp = b * (x * -a);
	} else if (y <= 6.2e-9) {
		tmp = x - (x * (a * b));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.4e+109:
		tmp = b * (x * -a)
	elif y <= 6.2e-9:
		tmp = x - (x * (a * b))
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.4e+109)
		tmp = Float64(b * Float64(x * Float64(-a)));
	elseif (y <= 6.2e-9)
		tmp = Float64(x - Float64(x * Float64(a * b)));
	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 <= -1.4e+109)
		tmp = b * (x * -a);
	elseif (y <= 6.2e-9)
		tmp = x - (x * (a * b));
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.4e+109], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-9], N[(x - N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4000000000000001e109

   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. Step-by-step derivation

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 31.7%

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

   6. Taylor expanded in z around 0 34.3%

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

      1. associate-*r* 34.3%

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

      2. mul-1-neg 34.3%

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

   8. Simplified 34.3%

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

   9. Taylor expanded in a around 0 19.0%

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

       1. mul-1-neg 19.0%

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

       2. unsub-neg 19.0%

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

       3. *-commutative 19.0%

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

   11. Simplified 19.0%

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

   12. Taylor expanded in a around inf 26.7%

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

       1. associate-*r* 29.0%

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

       2. associate-*r* 29.0%

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

       3. *-commutative 29.0%

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

       4. associate-*r* 29.0%

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

       5. associate-*r* 34.1%

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

       6. mul-1-neg 34.1%

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

   14. Simplified 34.1%

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

   if -1.4000000000000001e109 < y < 6.2000000000000001e-9

   1. Initial program 96.3%

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

      1. fma-define 96.3%

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

      2. sub-neg 96.3%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 75.1%

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

   6. Taylor expanded in z around 0 75.1%

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

      1. associate-*r* 75.1%

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

      2. mul-1-neg 75.1%

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

   8. Simplified 75.1%

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

   9. Taylor expanded in a around 0 39.7%

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

       1. mul-1-neg 39.7%

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

       2. unsub-neg 39.7%

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

       3. associate-*r* 40.9%

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

       4. *-commutative 40.9%

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

   11. Simplified 40.9%

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

   if 6.2000000000000001e-9 < y

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 35.6%

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

   6. Taylor expanded in z around 0 35.6%

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

      1. associate-*r* 35.6%

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

      2. mul-1-neg 35.6%

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

   8. Simplified 35.6%

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

   9. Taylor expanded in a around 0 7.3%

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

       1. mul-1-neg 7.3%

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

       2. unsub-neg 7.3%

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

       3. *-commutative 7.3%

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

   11. Simplified 7.3%

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

   12. Taylor expanded in a around inf 22.4%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-9}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.1% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-10}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.25e+109)
   (* b (* x (- a)))
   (if (<= y 5e-10) (- x (* a (* x b))) (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.25e+109) {
		tmp = b * (x * -a);
	} else if (y <= 5e-10) {
		tmp = x - (a * (x * b));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.25d+109)) then
        tmp = b * (x * -a)
    else if (y <= 5d-10) then
        tmp = x - (a * (x * b))
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.25e+109) {
		tmp = b * (x * -a);
	} else if (y <= 5e-10) {
		tmp = x - (a * (x * b));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.25e+109:
		tmp = b * (x * -a)
	elif y <= 5e-10:
		tmp = x - (a * (x * b))
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.25e+109)
		tmp = Float64(b * Float64(x * Float64(-a)));
	elseif (y <= 5e-10)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	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 <= -1.25e+109)
		tmp = b * (x * -a);
	elseif (y <= 5e-10)
		tmp = x - (a * (x * b));
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.25e+109], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-10], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e109

   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. Step-by-step derivation

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 31.7%

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

   6. Taylor expanded in z around 0 34.3%

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

      1. associate-*r* 34.3%

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

      2. mul-1-neg 34.3%

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

   8. Simplified 34.3%

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

   9. Taylor expanded in a around 0 19.0%

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

       1. mul-1-neg 19.0%

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

       2. unsub-neg 19.0%

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

       3. *-commutative 19.0%

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

   11. Simplified 19.0%

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

   12. Taylor expanded in a around inf 26.7%

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

       1. associate-*r* 29.0%

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

       2. associate-*r* 29.0%

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

       3. *-commutative 29.0%

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

       4. associate-*r* 29.0%

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

       5. associate-*r* 34.1%

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

       6. mul-1-neg 34.1%

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

   14. Simplified 34.1%

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

   if -1.25e109 < y < 5.00000000000000031e-10

   1. Initial program 96.3%

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

      1. fma-define 96.3%

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

      2. sub-neg 96.3%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 75.1%

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

   6. Taylor expanded in z around 0 75.1%

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

      1. associate-*r* 75.1%

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

      2. mul-1-neg 75.1%

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

   8. Simplified 75.1%

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

   9. Taylor expanded in a around 0 39.7%

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

       1. mul-1-neg 39.7%

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

       2. unsub-neg 39.7%

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

       3. *-commutative 39.7%

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

   11. Simplified 39.7%

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

   if 5.00000000000000031e-10 < y

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 35.6%

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

   6. Taylor expanded in z around 0 35.6%

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

      1. associate-*r* 35.6%

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

      2. mul-1-neg 35.6%

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

   8. Simplified 35.6%

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

   9. Taylor expanded in a around 0 7.3%

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

       1. mul-1-neg 7.3%

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

       2. unsub-neg 7.3%

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

       3. *-commutative 7.3%

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

   11. Simplified 7.3%

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

   12. Taylor expanded in a around inf 22.4%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-10}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 24.5% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-12} \lor \neg \left(a \leq 7.5 \cdot 10^{-83}\right):\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.2e-12) (not (<= a 7.5e-83))) (* x (* a (- b))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.2e-12) || !(a <= 7.5e-83)) {
		tmp = x * (a * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.2d-12)) .or. (.not. (a <= 7.5d-83))) then
        tmp = x * (a * -b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.2e-12) || !(a <= 7.5e-83)) {
		tmp = x * (a * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.2e-12) or not (a <= 7.5e-83):
		tmp = x * (a * -b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.2e-12) || !(a <= 7.5e-83))
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.2e-12) || ~((a <= 7.5e-83)))
		tmp = x * (a * -b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.2e-12], N[Not[LessEqual[a, 7.5e-83]], $MachinePrecision]], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -2.19999999999999992e-12 or 7.4999999999999997e-83 < a

   1. Initial program 96.1%

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

      1. fma-define 96.1%

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

      2. sub-neg 96.1%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 63.8%

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

   6. Taylor expanded in z around 0 64.4%

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

      1. associate-*r* 64.4%

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

      2. mul-1-neg 64.4%

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

   8. Simplified 64.4%

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

   9. Taylor expanded in a around 0 22.3%

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

       1. mul-1-neg 22.3%

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

       2. unsub-neg 22.3%

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

       3. *-commutative 22.3%

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

   11. Simplified 22.3%

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

   12. Taylor expanded in a around inf 26.8%

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

       1. associate-*r* 26.1%

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

       2. associate-*r* 26.1%

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

       3. *-commutative 26.1%

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

       4. associate-*r* 26.1%

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

       5. mul-1-neg 26.1%

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

   14. Simplified 26.1%

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

   if -2.19999999999999992e-12 < a < 7.4999999999999997e-83

   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. Step-by-step derivation

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 51.7%

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

   6. Taylor expanded in a around 0 34.2%

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

4. Final simplification 29.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-12} \lor \neg \left(a \leq 7.5 \cdot 10^{-83}\right):\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 23.1% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+48} \lor \neg \left(a \leq 1.3 \cdot 10^{-71}\right):\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.46e+48) (not (<= a 1.3e-71))) (* (* x t) (- y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.46e+48) || !(a <= 1.3e-71)) {
		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 ((a <= (-1.46d+48)) .or. (.not. (a <= 1.3d-71))) 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 ((a <= -1.46e+48) || !(a <= 1.3e-71)) {
		tmp = (x * t) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.46e+48) or not (a <= 1.3e-71):
		tmp = (x * t) * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.46e+48) || !(a <= 1.3e-71))
		tmp = Float64(Float64(x * 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 ((a <= -1.46e+48) || ~((a <= 1.3e-71)))
		tmp = (x * t) * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.46e+48], N[Not[LessEqual[a, 1.3e-71]], $MachinePrecision]], N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.46e48 or 1.2999999999999999e-71 < a

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 43.6%

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

      1. associate-*r* 43.6%

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

      2. neg-mul-1 43.6%

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

   8. Simplified 43.6%

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

   9. Taylor expanded in t around 0 14.2%

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

       1. mul-1-neg 14.2%

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

       2. unsub-neg 14.2%

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

       3. associate-*r* 12.9%

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

       4. *-commutative 12.9%

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

       5. *-commutative 12.9%

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

   11. Simplified 12.9%

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

   12. Taylor expanded in y around inf 19.4%

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

       1. mul-1-neg 19.4%

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

       2. associate-*r* 18.7%

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

       3. *-commutative 18.7%

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

   14. Simplified 18.7%

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

   if -1.46e48 < a < 1.2999999999999999e-71

   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. Step-by-step derivation

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 50.9%

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

   6. Taylor expanded in a around 0 33.0%

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

4. Final simplification 25.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+48} \lor \neg \left(a \leq 1.3 \cdot 10^{-71}\right):\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.1% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq 0.00017:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.2e+25)
   (* x (* y (- t)))
   (if (<= y 0.00017) x (* (* x t) (- y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.2e+25) {
		tmp = x * (y * -t);
	} else if (y <= 0.00017) {
		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 <= (-1.2d+25)) then
        tmp = x * (y * -t)
    else if (y <= 0.00017d0) 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 <= -1.2e+25) {
		tmp = x * (y * -t);
	} else if (y <= 0.00017) {
		tmp = x;
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.2e+25:
		tmp = x * (y * -t)
	elif y <= 0.00017:
		tmp = x
	else:
		tmp = (x * t) * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.2e+25)
		tmp = Float64(x * Float64(y * Float64(-t)));
	elseif (y <= 0.00017)
		tmp = x;
	else
		tmp = Float64(Float64(x * t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.2e+25)
		tmp = x * (y * -t);
	elseif (y <= 0.00017)
		tmp = x;
	else
		tmp = (x * t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.2e+25], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00017], x, N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.19999999999999998e25

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 56.4%

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

      1. associate-*r* 56.4%

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

      2. neg-mul-1 56.4%

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

   8. Simplified 56.4%

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

   9. Taylor expanded in t around 0 24.6%

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

       1. mul-1-neg 24.6%

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

       2. unsub-neg 24.6%

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

       3. associate-*r* 19.9%

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

       4. *-commutative 19.9%

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

       5. *-commutative 19.9%

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

   11. Simplified 19.9%

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

   12. Taylor expanded in y around inf 24.4%

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

       1. mul-1-neg 24.4%

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

       2. associate-*r* 19.6%

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

       3. *-commutative 19.6%

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

       4. associate-*r* 26.1%

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

       5. distribute-rgt-neg-in 26.1%

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

       6. distribute-rgt-neg-in 26.1%

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

   14. Simplified 26.1%

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

   if -1.19999999999999998e25 < y < 1.7e-4

   1. Initial program 95.7%

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

      1. fma-define 95.7%

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

      2. sub-neg 95.7%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 78.9%

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

   6. Taylor expanded in a around 0 31.5%

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

   if 1.7e-4 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 61.8%

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

      1. associate-*r* 61.8%

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

      2. neg-mul-1 61.8%

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

   8. Simplified 61.8%

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

   9. Taylor expanded in t around 0 8.7%

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

       1. mul-1-neg 8.7%

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

       2. unsub-neg 8.7%

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

       3. associate-*r* 8.8%

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

       4. *-commutative 8.8%

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

       5. *-commutative 8.8%

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

   11. Simplified 8.8%

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

   12. Taylor expanded in y around inf 9.0%

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

       1. mul-1-neg 9.0%

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

       2. associate-*r* 14.9%

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

       3. *-commutative 14.9%

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

   14. Simplified 14.9%

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

4. Final simplification 26.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq 0.00017:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.4% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 6.6e-8) (* x (- 1.0 (* a (+ z b)))) (* a (* x (- b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.6e-8) {
		tmp = x * (1.0 - (a * (z + b)));
	} 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 <= 6.6d-8) then
        tmp = x * (1.0d0 - (a * (z + b)))
    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 <= 6.6e-8) {
		tmp = x * (1.0 - (a * (z + b)));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 6.6e-8:
		tmp = x * (1.0 - (a * (z + b)))
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 6.6e-8)
		tmp = Float64(x * Float64(1.0 - Float64(a * Float64(z + b))));
	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 <= 6.6e-8)
		tmp = x * (1.0 - (a * (z + b)));
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 6.6e-8], N[(x * N[(1.0 - N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.59999999999999954e-8

   1. Initial program 97.0%

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

      1. fma-define 97.0%

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

      2. sub-neg 97.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 66.5%

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

   6. Taylor expanded in z around 0 71.5%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. mul-1-neg 100.0%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in a around 0 38.9%

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

       1. mul-1-neg 38.9%

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

       2. unsub-neg 38.9%

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

   11. Simplified 38.9%

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

   if 6.59999999999999954e-8 < y

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 35.6%

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

   6. Taylor expanded in z around 0 35.6%

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

      1. associate-*r* 35.6%

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

      2. mul-1-neg 35.6%

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

   8. Simplified 35.6%

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

   9. Taylor expanded in a around 0 7.3%

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

       1. mul-1-neg 7.3%

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

       2. unsub-neg 7.3%

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

       3. *-commutative 7.3%

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

   11. Simplified 7.3%

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

   12. Taylor expanded in a around inf 22.4%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 19.2% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

   1. fma-define 97.8%

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

   2. sub-neg 97.8%

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

   3. log1p-define 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 58.6%

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

6. Taylor expanded in a around 0 18.3%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024116 
(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))))))