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

Percentage Accurate: 96.6% → 99.5%

Time: 15.4s

Alternatives: 19

Speedup: 0.8×

• 41.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. fma-define 98.4%

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

   2. sub-neg 98.4%

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

   3. log1p-define 99.6%

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

3. Simplified 99.6%

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

Alternative 2: 90.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+36} \lor \neg \left(y \leq 2.4 \cdot 10^{+36}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right) - y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.5e+36) (not (<= y 2.4e+36)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (- (* a (- b)) (* y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.5e+36) || !(y <= 2.4e+36)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp(((a * -b) - (y * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.5d+36)) .or. (.not. (y <= 2.4d+36))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp(((a * -b) - (y * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.5e+36) || !(y <= 2.4e+36)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp(((a * -b) - (y * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.5e+36) or not (y <= 2.4e+36):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp(((a * -b) - (y * t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.5e+36) || !(y <= 2.4e+36))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(Float64(a * Float64(-b)) - Float64(y * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.5e+36) || ~((y <= 2.4e+36)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp(((a * -b) - (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.5e+36], N[Not[LessEqual[y, 2.4e+36]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(N[(a * (-b)), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5000000000000002e36 or 2.39999999999999992e36 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in y around inf 92.9%

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

   if -5.5000000000000002e36 < y < 2.39999999999999992e36

   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 97.8%

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

      1. neg-mul-1 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in t around inf 95.9%

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

      1. neg-mul-1 95.9%

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

   8. Simplified 95.9%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+36} \lor \neg \left(y \leq 2.4 \cdot 10^{+36}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right) - y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.1% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in z around 0 98.0%

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

   1. neg-mul-1 98.0%

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

5. Simplified 98.0%

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

6. Final simplification 98.0%

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

Alternative 4: 73.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-34} \lor \neg \left(a \leq 1.08 \cdot 10^{+27}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.8e-34) (not (<= a 1.08e+27)))
   (* x (exp (* a (- (- z) b))))
   (* x (exp (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.8e-34) || !(a <= 1.08e+27)) {
		tmp = x * exp((a * (-z - b)));
	} else {
		tmp = x * exp((y * -t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-4.8d-34)) .or. (.not. (a <= 1.08d+27))) then
        tmp = x * exp((a * (-z - b)))
    else
        tmp = x * exp((y * -t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.8e-34) || !(a <= 1.08e+27)) {
		tmp = x * Math.exp((a * (-z - b)));
	} else {
		tmp = x * Math.exp((y * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4.8e-34) or not (a <= 1.08e+27):
		tmp = x * math.exp((a * (-z - b)))
	else:
		tmp = x * math.exp((y * -t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4.8e-34) || !(a <= 1.08e+27))
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	else
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -4.8e-34) || ~((a <= 1.08e+27)))
		tmp = x * exp((a * (-z - b)));
	else
		tmp = x * exp((y * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4.8e-34], N[Not[LessEqual[a, 1.08e+27]], $MachinePrecision]], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.79999999999999982e-34 or 1.08e27 < a

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0 82.0%

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

      1. sub-neg 82.0%

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

      2. sub-neg 82.0%

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

      3. sub-neg 82.0%

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

      4. mul-1-neg 82.0%

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

      5. log1p-define 87.4%

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

      6. mul-1-neg 87.4%

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

   5. Simplified 87.4%

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

   6. Taylor expanded in z around 0 87.4%

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

      1. +-commutative 87.4%

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

      2. associate-*r* 87.4%

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

      3. associate-*r* 87.4%

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

      4. distribute-lft-out 87.4%

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

      5. mul-1-neg 87.4%

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

   8. Simplified 87.4%

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

   if -4.79999999999999982e-34 < a < 1.08e27

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. distribute-lft-neg-out 75.7%

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

      3. *-commutative 75.7%

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

   5. Simplified 75.7%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-34} \lor \neg \left(a \leq 1.08 \cdot 10^{+27}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+15} \lor \neg \left(t \leq 1.4 \cdot 10^{+90}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.6e+15) (not (<= t 1.4e+90)))
   (* x (exp (* y (- t))))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.6e+15) || !(t <= 1.4e+90)) {
		tmp = x * exp((y * -t));
	} else {
		tmp = x * exp((a * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.6d+15)) .or. (.not. (t <= 1.4d+90))) then
        tmp = x * exp((y * -t))
    else
        tmp = x * exp((a * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.6e+15) || !(t <= 1.4e+90)) {
		tmp = x * Math.exp((y * -t));
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.6e+15) or not (t <= 1.4e+90):
		tmp = x * math.exp((y * -t))
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.6e+15) || !(t <= 1.4e+90))
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.6e+15) || ~((t <= 1.4e+90)))
		tmp = x * exp((y * -t));
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.6e+15], N[Not[LessEqual[t, 1.4e+90]], $MachinePrecision]], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6e15 or 1.4e90 < t

   1. Initial program 97.2%

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

   3. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. distribute-lft-neg-out 84.9%

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

      3. *-commutative 84.9%

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

   5. Simplified 84.9%

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

   if -4.6e15 < t < 1.4e90

   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. Add Preprocessing

   3. Taylor expanded in b around inf 75.6%

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

      1. mul-1-neg 75.6%

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

      2. distribute-rgt-neg-out 75.6%

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

   5. Simplified 75.6%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+15} \lor \neg \left(t \leq 1.4 \cdot 10^{+90}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+46} \lor \neg \left(y \leq 3.1\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.6e+46) (not (<= y 3.1)))
   (* 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 <= -2.6e+46) || !(y <= 3.1)) {
		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 <= (-2.6d+46)) .or. (.not. (y <= 3.1d0))) 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 <= -2.6e+46) || !(y <= 3.1)) {
		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 <= -2.6e+46) or not (y <= 3.1):
		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 <= -2.6e+46) || !(y <= 3.1))
		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 <= -2.6e+46) || ~((y <= 3.1)))
		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, -2.6e+46], N[Not[LessEqual[y, 3.1]], $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 < -2.60000000000000013e46 or 3.10000000000000009 < y

   1. Initial program 98.3%

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

   3. Taylor expanded in y around inf 91.6%

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

   4. Taylor expanded in t around 0 63.8%

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

   if -2.60000000000000013e46 < y < 3.10000000000000009

   1. Initial program 97.7%

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

   3. Taylor expanded in b around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. distribute-rgt-neg-out 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+46} \lor \neg \left(y \leq 3.1\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+30} \lor \neg \left(y \leq 2.25\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.3e+30) (not (<= y 2.25)))
   (* 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 <= -1.3e+30) || !(y <= 2.25)) {
		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 <= (-1.3d+30)) .or. (.not. (y <= 2.25d0))) 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 <= -1.3e+30) || !(y <= 2.25)) {
		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 <= -1.3e+30) or not (y <= 2.25):
		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 <= -1.3e+30) || !(y <= 2.25))
		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 <= -1.3e+30) || ~((y <= 2.25)))
		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, -1.3e+30], N[Not[LessEqual[y, 2.25]], $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 < -1.29999999999999994e30 or 2.25 < y

   1. Initial program 98.3%

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

   3. Taylor expanded in y around inf 91.8%

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

   4. Taylor expanded in t around 0 63.1%

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

   if -1.29999999999999994e30 < y < 2.25

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 83.1%

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

      1. sub-neg 83.1%

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

      2. sub-neg 83.1%

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

      3. sub-neg 83.1%

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

      4. mul-1-neg 83.1%

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

      5. log1p-define 86.1%

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

      6. mul-1-neg 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in z around 0 86.1%

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

      1. +-commutative 86.1%

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

      2. associate-*r* 86.1%

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

      3. associate-*r* 86.1%

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

      4. distribute-lft-out 86.1%

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

      5. mul-1-neg 86.1%

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

   8. Simplified 86.1%

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

   9. Taylor expanded in a around 0 48.9%

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

       1. mul-1-neg 48.9%

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

       2. +-commutative 48.9%

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

       3. unsub-neg 48.9%

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

       4. +-commutative 48.9%

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

   11. Simplified 48.9%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+30} \lor \neg \left(y \leq 2.25\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in z around 0 98.0%

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

   1. neg-mul-1 98.0%

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

5. Simplified 98.0%

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

6. Taylor expanded in t around inf 88.2%

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

   1. neg-mul-1 88.2%

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

8. Simplified 88.2%

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

9. Final simplification 88.2%

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

Alternative 9: 33.9% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -45000000000000:\\ \;\;\;\;t \cdot \left(x \cdot \left(\frac{1}{t} - y\right)\right)\\ \mathbf{elif}\;y \leq 10^{+35}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t} \cdot \left(x \cdot t\right) - y \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -45000000000000.0)
   (* t (* x (- (/ 1.0 t) y)))
   (if (<= y 1e+35)
     (* x (- 1.0 (* a (+ z b))))
     (- (* (/ 1.0 t) (* x t)) (* y (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -45000000000000.0) {
		tmp = t * (x * ((1.0 / t) - y));
	} else if (y <= 1e+35) {
		tmp = x * (1.0 - (a * (z + b)));
	} else {
		tmp = ((1.0 / t) * (x * t)) - (y * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-45000000000000.0d0)) then
        tmp = t * (x * ((1.0d0 / t) - y))
    else if (y <= 1d+35) then
        tmp = x * (1.0d0 - (a * (z + b)))
    else
        tmp = ((1.0d0 / t) * (x * t)) - (y * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -45000000000000.0) {
		tmp = t * (x * ((1.0 / t) - y));
	} else if (y <= 1e+35) {
		tmp = x * (1.0 - (a * (z + b)));
	} else {
		tmp = ((1.0 / t) * (x * t)) - (y * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -45000000000000.0:
		tmp = t * (x * ((1.0 / t) - y))
	elif y <= 1e+35:
		tmp = x * (1.0 - (a * (z + b)))
	else:
		tmp = ((1.0 / t) * (x * t)) - (y * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -45000000000000.0)
		tmp = Float64(t * Float64(x * Float64(Float64(1.0 / t) - y)));
	elseif (y <= 1e+35)
		tmp = Float64(x * Float64(1.0 - Float64(a * Float64(z + b))));
	else
		tmp = Float64(Float64(Float64(1.0 / t) * Float64(x * t)) - Float64(y * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -45000000000000.0)
		tmp = t * (x * ((1.0 / t) - y));
	elseif (y <= 1e+35)
		tmp = x * (1.0 - (a * (z + b)));
	else
		tmp = ((1.0 / t) * (x * t)) - (y * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -45000000000000.0], N[(t * N[(x * N[(N[(1.0 / t), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+35], N[(x * N[(1.0 - N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / t), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision] - N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5e13

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. distribute-lft-neg-out 64.2%

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

      3. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in y around 0 21.4%

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

      1. mul-1-neg 21.4%

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

      2. *-commutative 21.4%

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

      3. unsub-neg 21.4%

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

   8. Simplified 21.4%

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

   9. Taylor expanded in t around inf 21.4%

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

   10. Taylor expanded in x around 0 29.7%

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

   if -4.5e13 < y < 9.9999999999999997e34

   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 y around 0 80.6%

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

      1. sub-neg 80.6%

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

      2. sub-neg 80.6%

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

      3. sub-neg 80.6%

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

      4. mul-1-neg 80.6%

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

      5. log1p-define 83.5%

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

      6. mul-1-neg 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in z around 0 83.5%

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

      1. +-commutative 83.5%

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

      2. associate-*r* 83.5%

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

      3. associate-*r* 83.5%

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

      4. distribute-lft-out 83.5%

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

      5. mul-1-neg 83.5%

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

   8. Simplified 83.5%

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

   9. Taylor expanded in a around 0 48.1%

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

       1. mul-1-neg 48.1%

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

       2. +-commutative 48.1%

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

       3. unsub-neg 48.1%

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

       4. +-commutative 48.1%

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

   11. Simplified 48.1%

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

   if 9.9999999999999997e34 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-lft-neg-out 63.9%

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

      3. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in y around 0 24.1%

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

      1. mul-1-neg 24.1%

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

      2. *-commutative 24.1%

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

      3. unsub-neg 24.1%

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

   8. Simplified 24.1%

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

   9. Taylor expanded in t around inf 24.1%

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

       1. associate-*r* 29.0%

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

       2. sub-neg 29.0%

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

       3. distribute-rgt-in 28.9%

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

   11. Applied egg-rr 28.9%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -45000000000000:\\ \;\;\;\;t \cdot \left(x \cdot \left(\frac{1}{t} - y\right)\right)\\ \mathbf{elif}\;y \leq 10^{+35}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t} \cdot \left(x \cdot t\right) - y \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 33.4% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -30000000000000:\\ \;\;\;\;t \cdot \left(x \cdot \left(\frac{1}{t} - y\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -30000000000000.0)
   (* t (* x (- (/ 1.0 t) y)))
   (if (<= y 6e+34) (* x (- 1.0 (* a (+ z b)))) (* x (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -30000000000000.0) {
		tmp = t * (x * ((1.0 / t) - y));
	} else if (y <= 6e+34) {
		tmp = x * (1.0 - (a * (z + b)));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-30000000000000.0d0)) then
        tmp = t * (x * ((1.0d0 / t) - y))
    else if (y <= 6d+34) then
        tmp = x * (1.0d0 - (a * (z + b)))
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -30000000000000.0) {
		tmp = t * (x * ((1.0 / t) - y));
	} else if (y <= 6e+34) {
		tmp = x * (1.0 - (a * (z + b)));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -30000000000000.0:
		tmp = t * (x * ((1.0 / t) - y))
	elif y <= 6e+34:
		tmp = x * (1.0 - (a * (z + b)))
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -30000000000000.0)
		tmp = Float64(t * Float64(x * Float64(Float64(1.0 / t) - y)));
	elseif (y <= 6e+34)
		tmp = Float64(x * Float64(1.0 - Float64(a * Float64(z + b))));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -30000000000000.0)
		tmp = t * (x * ((1.0 / t) - y));
	elseif (y <= 6e+34)
		tmp = x * (1.0 - (a * (z + b)));
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -30000000000000.0], N[(t * N[(x * N[(N[(1.0 / t), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+34], N[(x * N[(1.0 - N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e13

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. distribute-lft-neg-out 64.2%

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

      3. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in y around 0 21.4%

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

      1. mul-1-neg 21.4%

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

      2. *-commutative 21.4%

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

      3. unsub-neg 21.4%

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

   8. Simplified 21.4%

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

   9. Taylor expanded in t around inf 21.4%

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

   10. Taylor expanded in x around 0 29.7%

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

   if -3e13 < y < 6.00000000000000037e34

   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 y around 0 80.6%

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

      1. sub-neg 80.6%

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

      2. sub-neg 80.6%

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

      3. sub-neg 80.6%

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

      4. mul-1-neg 80.6%

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

      5. log1p-define 83.5%

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

      6. mul-1-neg 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in z around 0 83.5%

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

      1. +-commutative 83.5%

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

      2. associate-*r* 83.5%

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

      3. associate-*r* 83.5%

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

      4. distribute-lft-out 83.5%

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

      5. mul-1-neg 83.5%

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

   8. Simplified 83.5%

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

   9. Taylor expanded in a around 0 48.1%

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

       1. mul-1-neg 48.1%

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

       2. +-commutative 48.1%

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

       3. unsub-neg 48.1%

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

       4. +-commutative 48.1%

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

   11. Simplified 48.1%

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

   if 6.00000000000000037e34 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-lft-neg-out 63.9%

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

      3. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in y around 0 24.1%

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

      1. mul-1-neg 24.1%

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

      2. *-commutative 24.1%

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

      3. unsub-neg 24.1%

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

   8. Simplified 24.1%

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

   9. Taylor expanded in y around inf 25.1%

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

       1. mul-1-neg 25.1%

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

       2. *-commutative 25.1%

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

       3. distribute-rgt-neg-in 25.1%

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

       4. distribute-rgt-neg-in 25.1%

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

   11. Simplified 25.1%

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

   12. Taylor expanded in t around 0 25.1%

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

       1. mul-1-neg 25.1%

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

       2. associate-*r* 28.8%

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

       3. *-commutative 28.8%

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

       4. distribute-rgt-neg-out 28.8%

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

       5. associate-*l* 28.5%

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

   14. Simplified 28.5%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -30000000000000:\\ \;\;\;\;t \cdot \left(x \cdot \left(\frac{1}{t} - y\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 33.0% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(x \cdot \left(\frac{1}{t} - y\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.6e+14)
   (* t (* x (- (/ 1.0 t) y)))
   (if (<= y 5.2e+33) (* x (- 1.0 (* a b))) (* x (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.6e+14) {
		tmp = t * (x * ((1.0 / t) - y));
	} else if (y <= 5.2e+33) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9.6d+14)) then
        tmp = t * (x * ((1.0d0 / t) - y))
    else if (y <= 5.2d+33) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.6e+14) {
		tmp = t * (x * ((1.0 / t) - y));
	} else if (y <= 5.2e+33) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.6e+14:
		tmp = t * (x * ((1.0 / t) - y))
	elif y <= 5.2e+33:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.6e+14)
		tmp = Float64(t * Float64(x * Float64(Float64(1.0 / t) - y)));
	elseif (y <= 5.2e+33)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9.6e+14)
		tmp = t * (x * ((1.0 / t) - y));
	elseif (y <= 5.2e+33)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.6e+14], N[(t * N[(x * N[(N[(1.0 / t), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+33], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.6e14

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. distribute-lft-neg-out 64.2%

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

      3. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in y around 0 21.4%

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

      1. mul-1-neg 21.4%

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

      2. *-commutative 21.4%

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

      3. unsub-neg 21.4%

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

   8. Simplified 21.4%

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

   9. Taylor expanded in t around inf 21.4%

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

   10. Taylor expanded in x around 0 29.7%

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

   if -9.6e14 < y < 5.1999999999999995e33

   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 b around inf 80.6%

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

      1. mul-1-neg 80.6%

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

      2. distribute-rgt-neg-out 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in a around 0 46.5%

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

      1. neg-mul-1 46.5%

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

      2. unsub-neg 46.5%

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

   8. Simplified 46.5%

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

   if 5.1999999999999995e33 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-lft-neg-out 63.9%

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

      3. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in y around 0 24.1%

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

      1. mul-1-neg 24.1%

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

      2. *-commutative 24.1%

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

      3. unsub-neg 24.1%

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

   8. Simplified 24.1%

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

   9. Taylor expanded in y around inf 25.1%

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

       1. mul-1-neg 25.1%

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

       2. *-commutative 25.1%

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

       3. distribute-rgt-neg-in 25.1%

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

       4. distribute-rgt-neg-in 25.1%

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

   11. Simplified 25.1%

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

   12. Taylor expanded in t around 0 25.1%

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

       1. mul-1-neg 25.1%

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

       2. associate-*r* 28.8%

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

       3. *-commutative 28.8%

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

       4. distribute-rgt-neg-out 28.8%

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

       5. associate-*l* 28.5%

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

   14. Simplified 28.5%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(x \cdot \left(\frac{1}{t} - y\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.1% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(\frac{x}{b} - x \cdot a\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8e+81)
   (* b (- (/ x b) (* x a)))
   (if (<= y 3.1e+34) (* x (- 1.0 (* a b))) (* x (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e+81) {
		tmp = b * ((x / b) - (x * a));
	} else if (y <= 3.1e+34) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8d+81)) then
        tmp = b * ((x / b) - (x * a))
    else if (y <= 3.1d+34) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e+81) {
		tmp = b * ((x / b) - (x * a));
	} else if (y <= 3.1e+34) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8e+81:
		tmp = b * ((x / b) - (x * a))
	elif y <= 3.1e+34:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8e+81)
		tmp = Float64(b * Float64(Float64(x / b) - Float64(x * a)));
	elseif (y <= 3.1e+34)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8e+81)
		tmp = b * ((x / b) - (x * a));
	elseif (y <= 3.1e+34)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8e+81], N[(b * N[(N[(x / b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+34], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.99999999999999937e81

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 28.3%

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

      1. mul-1-neg 28.3%

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

      2. distribute-rgt-neg-out 28.3%

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

   5. Simplified 28.3%

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

   6. Taylor expanded in a around 0 7.9%

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

      1. mul-1-neg 7.9%

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

      2. unsub-neg 7.9%

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

   8. Simplified 7.9%

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

   9. Taylor expanded in b around inf 27.7%

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

   if -7.99999999999999937e81 < y < 3.09999999999999977e34

   1. Initial program 97.3%

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

   3. Taylor expanded in b around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. distribute-rgt-neg-out 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in a around 0 43.3%

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

      1. neg-mul-1 43.3%

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

      2. unsub-neg 43.3%

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

   8. Simplified 43.3%

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

   if 3.09999999999999977e34 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-lft-neg-out 63.9%

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

      3. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in y around 0 24.1%

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

      1. mul-1-neg 24.1%

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

      2. *-commutative 24.1%

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

      3. unsub-neg 24.1%

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

   8. Simplified 24.1%

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

   9. Taylor expanded in y around inf 25.1%

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

       1. mul-1-neg 25.1%

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

       2. *-commutative 25.1%

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

       3. distribute-rgt-neg-in 25.1%

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

       4. distribute-rgt-neg-in 25.1%

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

   11. Simplified 25.1%

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

   12. Taylor expanded in t around 0 25.1%

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

       1. mul-1-neg 25.1%

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

       2. associate-*r* 28.8%

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

       3. *-commutative 28.8%

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

       4. distribute-rgt-neg-out 28.8%

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

       5. associate-*l* 28.5%

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

   14. Simplified 28.5%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(\frac{x}{b} - x \cdot a\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+126}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.15e+126)
   (- x (* t (* x y)))
   (if (<= y 2.7e+34) (* x (- 1.0 (* a b))) (* x (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.15e+126) {
		tmp = x - (t * (x * y));
	} else if (y <= 2.7e+34) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.15d+126)) then
        tmp = x - (t * (x * y))
    else if (y <= 2.7d+34) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.15e+126) {
		tmp = x - (t * (x * y));
	} else if (y <= 2.7e+34) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.15e+126:
		tmp = x - (t * (x * y))
	elif y <= 2.7e+34:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.15e+126)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (y <= 2.7e+34)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.15e+126)
		tmp = x - (t * (x * y));
	elseif (y <= 2.7e+34)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.15e+126], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+34], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15e126

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. distribute-lft-neg-out 59.8%

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

      3. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in y around 0 33.6%

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

      1. mul-1-neg 33.6%

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

      2. unsub-neg 33.6%

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

      3. associate-*r* 30.9%

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

   8. Simplified 30.9%

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

   9. Taylor expanded in t around 0 33.6%

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

       1. *-commutative 33.6%

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

   11. Simplified 33.6%

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

   if -1.15e126 < y < 2.7e34

   1. Initial program 97.5%

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

   3. Taylor expanded in b around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. distribute-rgt-neg-out 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in a around 0 41.1%

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

      1. neg-mul-1 41.1%

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

      2. unsub-neg 41.1%

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

   8. Simplified 41.1%

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

   if 2.7e34 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-lft-neg-out 63.9%

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

      3. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in y around 0 24.1%

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

      1. mul-1-neg 24.1%

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

      2. *-commutative 24.1%

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

      3. unsub-neg 24.1%

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

   8. Simplified 24.1%

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

   9. Taylor expanded in y around inf 25.1%

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

       1. mul-1-neg 25.1%

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

       2. *-commutative 25.1%

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

       3. distribute-rgt-neg-in 25.1%

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

       4. distribute-rgt-neg-in 25.1%

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

   11. Simplified 25.1%

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

   12. Taylor expanded in t around 0 25.1%

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

       1. mul-1-neg 25.1%

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

       2. associate-*r* 28.8%

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

       3. *-commutative 28.8%

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

       4. distribute-rgt-neg-out 28.8%

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

       5. associate-*l* 28.5%

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

   14. Simplified 28.5%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+126}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.0% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+126}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.8e+126)
   (* (- t) (* x y))
   (if (<= y 2e+34) (* x (- 1.0 (* a b))) (* x (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.8e+126) {
		tmp = -t * (x * y);
	} else if (y <= 2e+34) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9.8d+126)) then
        tmp = -t * (x * y)
    else if (y <= 2d+34) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.8e+126) {
		tmp = -t * (x * y);
	} else if (y <= 2e+34) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.8e+126:
		tmp = -t * (x * y)
	elif y <= 2e+34:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.8e+126)
		tmp = Float64(Float64(-t) * Float64(x * y));
	elseif (y <= 2e+34)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9.8e+126)
		tmp = -t * (x * y);
	elseif (y <= 2e+34)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.8e+126], N[((-t) * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+34], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.80000000000000002e126

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. distribute-lft-neg-out 59.8%

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

      3. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in y around 0 30.9%

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

      1. mul-1-neg 30.9%

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

      2. *-commutative 30.9%

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

      3. unsub-neg 30.9%

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

   8. Simplified 30.9%

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

   9. Taylor expanded in y around inf 33.3%

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

       1. mul-1-neg 33.3%

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

       2. *-commutative 33.3%

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

       3. distribute-rgt-neg-in 33.3%

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

       4. distribute-rgt-neg-in 33.3%

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

   11. Simplified 33.3%

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

   if -9.80000000000000002e126 < y < 1.99999999999999989e34

   1. Initial program 97.5%

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

   3. Taylor expanded in b around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. distribute-rgt-neg-out 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in a around 0 41.1%

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

      1. neg-mul-1 41.1%

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

      2. unsub-neg 41.1%

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

   8. Simplified 41.1%

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

   if 1.99999999999999989e34 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-lft-neg-out 63.9%

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

      3. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in y around 0 24.1%

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

      1. mul-1-neg 24.1%

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

      2. *-commutative 24.1%

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

      3. unsub-neg 24.1%

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

   8. Simplified 24.1%

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

   9. Taylor expanded in y around inf 25.1%

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

       1. mul-1-neg 25.1%

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

       2. *-commutative 25.1%

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

       3. distribute-rgt-neg-in 25.1%

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

       4. distribute-rgt-neg-in 25.1%

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

   11. Simplified 25.1%

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

   12. Taylor expanded in t around 0 25.1%

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

       1. mul-1-neg 25.1%

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

       2. associate-*r* 28.8%

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

       3. *-commutative 28.8%

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

       4. distribute-rgt-neg-out 28.8%

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

       5. associate-*l* 28.5%

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

   14. Simplified 28.5%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+126}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.6% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-9} \lor \neg \left(y \leq 3.1 \cdot 10^{-63}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.6e-9) (not (<= y 3.1e-63))) (* a (* x (- b))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.6e-9) || !(y <= 3.1e-63)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.6d-9)) .or. (.not. (y <= 3.1d-63))) then
        tmp = a * (x * -b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.6e-9) || !(y <= 3.1e-63)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.6e-9) or not (y <= 3.1e-63):
		tmp = a * (x * -b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.6e-9) || !(y <= 3.1e-63))
		tmp = Float64(a * Float64(x * Float64(-b)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.6e-9) || ~((y <= 3.1e-63)))
		tmp = a * (x * -b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.6e-9], N[Not[LessEqual[y, 3.1e-63]], $MachinePrecision]], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.60000000000000037e-9 or 3.09999999999999984e-63 < y

   1. Initial program 97.8%

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

   3. Taylor expanded in b around inf 41.2%

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

      1. mul-1-neg 41.2%

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

      2. distribute-rgt-neg-out 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in a around 0 10.8%

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

      1. mul-1-neg 10.8%

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

      2. unsub-neg 10.8%

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

   8. Simplified 10.8%

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

   9. Taylor expanded in a around inf 20.6%

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

       1. mul-1-neg 20.6%

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

       2. distribute-rgt-neg-in 20.6%

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

       3. distribute-rgt-neg-in 20.6%

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

   11. Simplified 20.6%

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

   if -6.60000000000000037e-9 < y < 3.09999999999999984e-63

   1. Initial program 98.1%

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

   3. Taylor expanded in b around inf 84.3%

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

      1. mul-1-neg 84.3%

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

      2. distribute-rgt-neg-out 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in a around 0 36.0%

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

4. Final simplification 27.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-9} \lor \neg \left(y \leq 3.1 \cdot 10^{-63}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 26.5% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+46}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.6e+46)
   (* (- t) (* x y))
   (if (<= y 1.12e-38) x (* x (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.6e+46) {
		tmp = -t * (x * y);
	} else if (y <= 1.12e-38) {
		tmp = x;
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.6d+46)) then
        tmp = -t * (x * y)
    else if (y <= 1.12d-38) then
        tmp = x
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.6e+46) {
		tmp = -t * (x * y);
	} else if (y <= 1.12e-38) {
		tmp = x;
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.6e+46:
		tmp = -t * (x * y)
	elif y <= 1.12e-38:
		tmp = x
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.6e+46)
		tmp = Float64(Float64(-t) * Float64(x * y));
	elseif (y <= 1.12e-38)
		tmp = x;
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.6e+46)
		tmp = -t * (x * y);
	elseif (y <= 1.12e-38)
		tmp = x;
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.6e+46], N[((-t) * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e-38], x, N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.60000000000000013e46

   1. Initial program 98.1%

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

   3. Taylor expanded in t around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. distribute-lft-neg-out 64.4%

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

      3. *-commutative 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in y around 0 23.2%

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

      1. mul-1-neg 23.2%

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

      2. *-commutative 23.2%

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

      3. unsub-neg 23.2%

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

   8. Simplified 23.2%

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

   9. Taylor expanded in y around inf 24.5%

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

       1. mul-1-neg 24.5%

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

       2. *-commutative 24.5%

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

       3. distribute-rgt-neg-in 24.5%

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

       4. distribute-rgt-neg-in 24.5%

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

   11. Simplified 24.5%

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

   if -2.60000000000000013e46 < y < 1.1200000000000001e-38

   1. Initial program 98.3%

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

   3. Taylor expanded in b around inf 82.7%

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

      1. mul-1-neg 82.7%

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

      2. distribute-rgt-neg-out 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in a around 0 33.9%

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

   if 1.1200000000000001e-38 < y

   1. Initial program 97.3%

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

   3. Taylor expanded in t around inf 56.6%

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

      1. mul-1-neg 56.6%

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

      2. distribute-lft-neg-out 56.6%

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

      3. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in y around 0 19.9%

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

      1. mul-1-neg 19.9%

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

      2. *-commutative 19.9%

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

      3. unsub-neg 19.9%

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

   8. Simplified 19.9%

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

   9. Taylor expanded in y around inf 23.8%

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

       1. mul-1-neg 23.8%

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

       2. *-commutative 23.8%

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

       3. distribute-rgt-neg-in 23.8%

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

       4. distribute-rgt-neg-in 23.8%

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

   11. Simplified 23.8%

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

   12. Taylor expanded in t around 0 23.8%

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

       1. mul-1-neg 23.8%

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

       2. associate-*r* 26.7%

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

       3. *-commutative 26.7%

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

       4. distribute-rgt-neg-out 26.7%

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

       5. associate-*l* 26.4%

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

   14. Simplified 26.4%

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

4. Final simplification 29.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+46}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 27.4% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+42}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.2e+42)
   (* (- t) (* x y))
   (if (<= y 2.6e-67) x (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.2e+42) {
		tmp = -t * (x * y);
	} else if (y <= 2.6e-67) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8.2d+42)) then
        tmp = -t * (x * y)
    else if (y <= 2.6d-67) then
        tmp = x
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.2e+42) {
		tmp = -t * (x * y);
	} else if (y <= 2.6e-67) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.2e+42:
		tmp = -t * (x * y)
	elif y <= 2.6e-67:
		tmp = x
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.2e+42)
		tmp = Float64(Float64(-t) * Float64(x * y));
	elseif (y <= 2.6e-67)
		tmp = x;
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8.2e+42)
		tmp = -t * (x * y);
	elseif (y <= 2.6e-67)
		tmp = x;
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.2e+42], N[((-t) * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-67], x, N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.2000000000000001e42

   1. Initial program 98.1%

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

   3. Taylor expanded in t around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. distribute-lft-neg-out 64.4%

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

      3. *-commutative 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in y around 0 23.2%

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

      1. mul-1-neg 23.2%

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

      2. *-commutative 23.2%

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

      3. unsub-neg 23.2%

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

   8. Simplified 23.2%

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

   9. Taylor expanded in y around inf 24.5%

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

       1. mul-1-neg 24.5%

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

       2. *-commutative 24.5%

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

       3. distribute-rgt-neg-in 24.5%

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

       4. distribute-rgt-neg-in 24.5%

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

   11. Simplified 24.5%

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

   if -8.2000000000000001e42 < y < 2.5999999999999999e-67

   1. Initial program 98.2%

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

   3. Taylor expanded in b around inf 82.9%

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

      1. mul-1-neg 82.9%

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

      2. distribute-rgt-neg-out 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in a around 0 34.2%

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

   if 2.5999999999999999e-67 < y

   1. Initial program 97.5%

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

   3. Taylor expanded in b around inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. distribute-rgt-neg-out 47.3%

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

   5. Simplified 47.3%

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

   6. Taylor expanded in a around 0 12.7%

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

      1. mul-1-neg 12.7%

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

      2. unsub-neg 12.7%

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

   8. Simplified 12.7%

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

   9. Taylor expanded in a around inf 24.0%

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

       1. mul-1-neg 24.0%

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

       2. distribute-rgt-neg-in 24.0%

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

       3. distribute-rgt-neg-in 24.0%

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

   11. Simplified 24.0%

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

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+42}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 20.3% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-9} \lor \neg \left(y \leq 2.5 \cdot 10^{-37}\right):\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.2e-9) (not (<= y 2.5e-37))) (* t (* x y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.2e-9) || !(y <= 2.5e-37)) {
		tmp = t * (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9.2d-9)) .or. (.not. (y <= 2.5d-37))) then
        tmp = t * (x * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.2e-9) || !(y <= 2.5e-37)) {
		tmp = t * (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9.2e-9) or not (y <= 2.5e-37):
		tmp = t * (x * y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9.2e-9) || !(y <= 2.5e-37))
		tmp = Float64(t * Float64(x * y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9.2e-9) || ~((y <= 2.5e-37)))
		tmp = t * (x * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9.2e-9], N[Not[LessEqual[y, 2.5e-37]], $MachinePrecision]], N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.1999999999999997e-9 or 2.4999999999999999e-37 < y

   1. Initial program 97.8%

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

   3. Taylor expanded in t around inf 59.7%

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

      1. mul-1-neg 59.7%

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

      2. distribute-lft-neg-out 59.7%

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

      3. *-commutative 59.7%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in y around 0 20.2%

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

      1. mul-1-neg 20.2%

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

      2. *-commutative 20.2%

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

      3. unsub-neg 20.2%

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

   8. Simplified 20.2%

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

   9. Taylor expanded in y around inf 23.0%

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

       1. mul-1-neg 23.0%

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

       2. *-commutative 23.0%

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

       3. distribute-rgt-neg-in 23.0%

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

       4. distribute-rgt-neg-in 23.0%

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

   11. Simplified 23.0%

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

       1. add-sqr-sqrt 10.7%

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

       2. sqrt-unprod 23.9%

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

       3. sqr-neg 23.9%

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

       4. sqrt-unprod 5.2%

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

       5. add-sqr-sqrt 13.4%

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

       6. pow1 13.4%

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

       7. *-commutative 13.4%

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

   13. Applied egg-rr 13.4%

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

       1. unpow1 13.4%

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

   15. Simplified 13.4%

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

   if -9.1999999999999997e-9 < y < 2.4999999999999999e-37

   1. Initial program 98.2%

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

   3. Taylor expanded in b around inf 84.0%

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

      1. mul-1-neg 84.0%

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

      2. distribute-rgt-neg-out 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in a around 0 35.7%

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

4. Final simplification 24.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-9} \lor \neg \left(y \leq 2.5 \cdot 10^{-37}\right):\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 18.8% 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 98.0%

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

3. Taylor expanded in b around inf 61.2%

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

   1. mul-1-neg 61.2%

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

   2. distribute-rgt-neg-out 61.2%

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

5. Simplified 61.2%

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

6. Taylor expanded in a around 0 19.4%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024135 
(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))))))