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

Percentage Accurate: 96.5% → 99.6%

Time: 27.6s

Alternatives: 17

Speedup: 0.8×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.2%

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

   1. +-commutative 94.2%

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

   2. fma-def 94.6%

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

   3. sub-neg 94.6%

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

   4. log1p-def 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 96.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+268}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5e+268)
   (* x (exp (* a (- (- b) z))))
   (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5e+268) {
		tmp = x * exp((a * (-b - z)));
	} else {
		tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-5d+268)) then
        tmp = x * exp((a * (-b - z)))
    else
        tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5e+268) {
		tmp = x * Math.exp((a * (-b - z)));
	} else {
		tmp = x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5e+268:
		tmp = x * math.exp((a * (-b - z)))
	else:
		tmp = x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5e+268)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-b) - z))));
	else
		tmp = Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5e+268)
		tmp = x * exp((a * (-b - z)));
	else
		tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5e+268], N[(x * N[Exp[N[(a * N[((-b) - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.0000000000000002e268

   1. Initial program 17.7%

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

   2. Taylor expanded in y around 0 34.4%

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

      1. sub-neg 34.4%

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

      2. neg-mul-1 34.4%

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

      3. log1p-def 100.0%

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

      4. neg-mul-1 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. associate-*r* 100.0%

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

      4. neg-mul-1 100.0%

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

      5. distribute-lft-out 100.0%

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

   7. Simplified 100.0%

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

   if -5.0000000000000002e268 < a

   1. Initial program 96.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+268}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\\ \end{array} \]

Alternative 3: 86.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+18} \lor \neg \left(y \leq 4.5\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.45e+18) (not (<= y 4.5)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (- b) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e+18) || !(y <= 4.5)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * (-b - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.45d+18)) .or. (.not. (y <= 4.5d0))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((a * (-b - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e+18) || !(y <= 4.5)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * (-b - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.45e+18) or not (y <= 4.5):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * (-b - z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.45e+18) || !(y <= 4.5))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-b) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.45e+18) || ~((y <= 4.5)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((a * (-b - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.45e+18], N[Not[LessEqual[y, 4.5]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[((-b) - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e18 or 4.5 < y

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 87.3%

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

   if -1.45e18 < y < 4.5

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 77.6%

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

      1. sub-neg 77.6%

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

      2. neg-mul-1 77.6%

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

      3. log1p-def 86.1%

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

      4. neg-mul-1 86.1%

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

   4. Simplified 86.1%

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

   5. Taylor expanded in z around 0 86.1%

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

      1. associate-*r* 86.1%

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

      2. neg-mul-1 86.1%

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

      3. associate-*r* 86.1%

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

      4. neg-mul-1 86.1%

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

      5. distribute-lft-out 86.1%

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

   7. Simplified 86.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+18} \lor \neg \left(y \leq 4.5\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \end{array} \]

Alternative 4: 72.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+15} \lor \neg \left(a \leq 1.1 \cdot 10^{-105}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.9e+15) (not (<= a 1.1e-105)))
   (* x (exp (* a (- (- b) z))))
   (* x (exp (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.9e+15) || !(a <= 1.1e-105)) {
		tmp = x * exp((a * (-b - z)));
	} 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 <= (-1.9d+15)) .or. (.not. (a <= 1.1d-105))) then
        tmp = x * exp((a * (-b - z)))
    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 <= -1.9e+15) || !(a <= 1.1e-105)) {
		tmp = x * Math.exp((a * (-b - z)));
	} else {
		tmp = x * Math.exp((y * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.9e+15) or not (a <= 1.1e-105):
		tmp = x * math.exp((a * (-b - z)))
	else:
		tmp = x * math.exp((y * -t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.9e+15) || !(a <= 1.1e-105))
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-b) - z))));
	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 <= -1.9e+15) || ~((a <= 1.1e-105)))
		tmp = x * exp((a * (-b - z)));
	else
		tmp = x * exp((y * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.9e+15], N[Not[LessEqual[a, 1.1e-105]], $MachinePrecision]], N[(x * N[Exp[N[(a * N[((-b) - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9e15 or 1.10000000000000002e-105 < a

   1. Initial program 90.7%

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

   2. Taylor expanded in y around 0 67.8%

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

      1. sub-neg 67.8%

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

      2. neg-mul-1 67.8%

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

      3. log1p-def 79.9%

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

      4. neg-mul-1 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in z around 0 79.9%

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

      1. associate-*r* 79.9%

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

      2. neg-mul-1 79.9%

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

      3. associate-*r* 79.9%

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

      4. neg-mul-1 79.9%

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

      5. distribute-lft-out 79.9%

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

   7. Simplified 79.9%

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

   if -1.9e15 < a < 1.10000000000000002e-105

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.0%

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

      1. mul-1-neg 76.0%

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

      2. distribute-lft-neg-out 76.0%

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

      3. *-commutative 76.0%

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

   4. Simplified 76.0%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+15} \lor \neg \left(a \leq 1.1 \cdot 10^{-105}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 5: 50.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-304}:\\ \;\;\;\;\left(x \cdot \left(z \cdot z\right)\right) \cdot \left(a \cdot -0.5\right)\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-15}:\\ \;\;\;\;x - \left(z + b\right) \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -4.5e+19)
     t_1
     (if (<= y 5.8e-304)
       (* (* x (* z z)) (* a -0.5))
       (if (<= y 3.05e-15) (- x (* (+ z b) (* x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -4.5e+19) {
		tmp = t_1;
	} else if (y <= 5.8e-304) {
		tmp = (x * (z * z)) * (a * -0.5);
	} else if (y <= 3.05e-15) {
		tmp = x - ((z + b) * (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-4.5d+19)) then
        tmp = t_1
    else if (y <= 5.8d-304) then
        tmp = (x * (z * z)) * (a * (-0.5d0))
    else if (y <= 3.05d-15) then
        tmp = x - ((z + b) * (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -4.5e+19) {
		tmp = t_1;
	} else if (y <= 5.8e-304) {
		tmp = (x * (z * z)) * (a * -0.5);
	} else if (y <= 3.05e-15) {
		tmp = x - ((z + b) * (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -4.5e+19:
		tmp = t_1
	elif y <= 5.8e-304:
		tmp = (x * (z * z)) * (a * -0.5)
	elif y <= 3.05e-15:
		tmp = x - ((z + b) * (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -4.5e+19)
		tmp = t_1;
	elseif (y <= 5.8e-304)
		tmp = Float64(Float64(x * Float64(z * z)) * Float64(a * -0.5));
	elseif (y <= 3.05e-15)
		tmp = Float64(x - Float64(Float64(z + b) * Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -4.5e+19)
		tmp = t_1;
	elseif (y <= 5.8e-304)
		tmp = (x * (z * z)) * (a * -0.5);
	elseif (y <= 3.05e-15)
		tmp = x - ((z + b) * (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+19], t$95$1, If[LessEqual[y, 5.8e-304], N[(N[(x * N[(z * z), $MachinePrecision]), $MachinePrecision] * N[(a * -0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.05e-15], N[(x - N[(N[(z + b), $MachinePrecision] * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5e19 or 3.04999999999999986e-15 < y

   1. Initial program 95.8%

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

   2. Taylor expanded in y around inf 85.7%

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

   3. Taylor expanded in t around 0 68.0%

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

   if -4.5e19 < y < 5.8e-304

   1. Initial program 94.3%

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

   2. Taylor expanded in y around 0 71.9%

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

      1. sub-neg 71.9%

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

      2. neg-mul-1 71.9%

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

      3. log1p-def 80.2%

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

      4. neg-mul-1 80.2%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in a around 0 23.8%

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

      1. +-commutative 23.8%

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

      2. associate-*r* 22.5%

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

      3. fma-def 22.5%

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

      4. sub-neg 22.5%

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

      5. log1p-def 23.9%

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

   7. Simplified 23.9%

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

   8. Taylor expanded in z around 0 23.8%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(a \cdot \left(b \cdot x\right)\right) + \left(-1 \cdot \left(a \cdot \left(x \cdot z\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right)\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 23.8%

         \[\leadsto x + \left(\color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} + \left(-1 \cdot \left(a \cdot \left(x \cdot z\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right)\right) \]

      2. associate-+r+ 23.8%

         \[\leadsto x + \color{blue}{\left(\left(\left(-a \cdot \left(b \cdot x\right)\right) + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right)} \]

      3. neg-mul-1 23.8%

         \[\leadsto x + \left(\left(\color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      4. distribute-lft-out 23.8%

         \[\leadsto x + \left(\color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right) + a \cdot \left(x \cdot z\right)\right)} + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      5. distribute-lft-in 25.2%

         \[\leadsto x + \left(-1 \cdot \color{blue}{\left(a \cdot \left(b \cdot x + x \cdot z\right)\right)} + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      6. *-commutative 25.2%

         \[\leadsto x + \left(-1 \cdot \left(a \cdot \left(\color{blue}{x \cdot b} + x \cdot z\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      7. distribute-lft-in 25.2%

         \[\leadsto x + \left(-1 \cdot \left(a \cdot \color{blue}{\left(x \cdot \left(b + z\right)\right)}\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      8. associate-+r+ 25.2%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(a \cdot \left(x \cdot \left(b + z\right)\right)\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)} \]

   10. Simplified 23.9%

       \[\leadsto \color{blue}{\left(x - \left(b + z\right) \cdot \left(a \cdot x\right)\right) + -0.5 \cdot \left(x \cdot \left(a \cdot \left(z \cdot z\right)\right)\right)} \]

   11. Taylor expanded in z around inf 37.6%

       \[\leadsto \color{blue}{-0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 37.6%

          \[\leadsto \color{blue}{\left(-0.5 \cdot a\right) \cdot \left(x \cdot {z}^{2}\right)} \]

       2. *-commutative 37.6%

          \[\leadsto \color{blue}{\left(x \cdot {z}^{2}\right) \cdot \left(-0.5 \cdot a\right)} \]

       3. unpow2 37.6%

          \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot z\right)}\right) \cdot \left(-0.5 \cdot a\right) \]

       4. *-commutative 37.6%

          \[\leadsto \left(x \cdot \left(z \cdot z\right)\right) \cdot \color{blue}{\left(a \cdot -0.5\right)} \]

   13. Simplified 37.6%

       \[\leadsto \color{blue}{\left(x \cdot \left(z \cdot z\right)\right) \cdot \left(a \cdot -0.5\right)} \]

   if 5.8e-304 < y < 3.04999999999999986e-15

   1. Initial program 91.2%

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

   2. Taylor expanded in y around 0 81.7%

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

      1. sub-neg 81.7%

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

      2. neg-mul-1 81.7%

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

      3. log1p-def 90.4%

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

      4. neg-mul-1 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in z around 0 90.4%

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

      1. associate-*r* 90.4%

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

      2. neg-mul-1 90.4%

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

      3. associate-*r* 90.4%

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

      4. neg-mul-1 90.4%

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

      5. distribute-lft-out 90.4%

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

   7. Simplified 90.4%

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

   8. Taylor expanded in a around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

      3. *-commutative 51.4%

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

      4. *-commutative 51.4%

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

      5. associate-*l* 51.3%

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

      6. *-commutative 51.3%

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

   10. Simplified 51.3%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+19}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-304}:\\ \;\;\;\;\left(x \cdot \left(z \cdot z\right)\right) \cdot \left(a \cdot -0.5\right)\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-15}:\\ \;\;\;\;x - \left(z + b\right) \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 6: 73.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+24} \lor \neg \left(y \leq 0.7\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2e+24) (not (<= y 0.7)))
   (* 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 <= -2e+24) || !(y <= 0.7)) {
		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 <= (-2d+24)) .or. (.not. (y <= 0.7d0))) 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 <= -2e+24) || !(y <= 0.7)) {
		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 <= -2e+24) or not (y <= 0.7):
		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 <= -2e+24) || !(y <= 0.7))
		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 <= -2e+24) || ~((y <= 0.7)))
		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, -2e+24], N[Not[LessEqual[y, 0.7]], $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 < -2e24 or 0.69999999999999996 < y

   1. Initial program 95.6%

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

   2. Taylor expanded in y around inf 86.9%

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

   3. Taylor expanded in t around 0 69.5%

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

   if -2e24 < y < 0.69999999999999996

   1. Initial program 93.0%

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

   2. Taylor expanded in b around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. distribute-rgt-neg-out 74.7%

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

   4. Simplified 74.7%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+24} \lor \neg \left(y \leq 0.7\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 7: 72.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+47} \lor \neg \left(t \leq 1.45 \cdot 10^{-74}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9.4e+47) (not (<= t 1.45e-74)))
   (* 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 <= -9.4e+47) || !(t <= 1.45e-74)) {
		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 <= (-9.4d+47)) .or. (.not. (t <= 1.45d-74))) 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 <= -9.4e+47) || !(t <= 1.45e-74)) {
		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 <= -9.4e+47) or not (t <= 1.45e-74):
		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 <= -9.4e+47) || !(t <= 1.45e-74))
		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 <= -9.4e+47) || ~((t <= 1.45e-74)))
		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, -9.4e+47], N[Not[LessEqual[t, 1.45e-74]], $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 < -9.39999999999999928e47 or 1.45e-74 < t

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-lft-neg-out 76.2%

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

      3. *-commutative 76.2%

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

   4. Simplified 76.2%

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

   if -9.39999999999999928e47 < t < 1.45e-74

   1. Initial program 93.7%

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

   2. Taylor expanded in b around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-rgt-neg-out 70.8%

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

   4. Simplified 70.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+47} \lor \neg \left(t \leq 1.45 \cdot 10^{-74}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 8: 24.4% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;y \leq -0.00036:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-304}:\\ \;\;\;\;-x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* x (- a)))))
   (if (<= y -0.00036)
     t_1
     (if (<= y -4.6e-217)
       x
       (if (<= y 5.5e-304) (- (* x (* y t))) (if (<= y 5e+19) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (x * -a);
	double tmp;
	if (y <= -0.00036) {
		tmp = t_1;
	} else if (y <= -4.6e-217) {
		tmp = x;
	} else if (y <= 5.5e-304) {
		tmp = -(x * (y * t));
	} else if (y <= 5e+19) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (x * -a)
    if (y <= (-0.00036d0)) then
        tmp = t_1
    else if (y <= (-4.6d-217)) then
        tmp = x
    else if (y <= 5.5d-304) then
        tmp = -(x * (y * t))
    else if (y <= 5d+19) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (x * -a);
	double tmp;
	if (y <= -0.00036) {
		tmp = t_1;
	} else if (y <= -4.6e-217) {
		tmp = x;
	} else if (y <= 5.5e-304) {
		tmp = -(x * (y * t));
	} else if (y <= 5e+19) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (x * -a)
	tmp = 0
	if y <= -0.00036:
		tmp = t_1
	elif y <= -4.6e-217:
		tmp = x
	elif y <= 5.5e-304:
		tmp = -(x * (y * t))
	elif y <= 5e+19:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(x * Float64(-a)))
	tmp = 0.0
	if (y <= -0.00036)
		tmp = t_1;
	elseif (y <= -4.6e-217)
		tmp = x;
	elseif (y <= 5.5e-304)
		tmp = Float64(-Float64(x * Float64(y * t)));
	elseif (y <= 5e+19)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (x * -a);
	tmp = 0.0;
	if (y <= -0.00036)
		tmp = t_1;
	elseif (y <= -4.6e-217)
		tmp = x;
	elseif (y <= 5.5e-304)
		tmp = -(x * (y * t));
	elseif (y <= 5e+19)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.00036], t$95$1, If[LessEqual[y, -4.6e-217], x, If[LessEqual[y, 5.5e-304], (-N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), If[LessEqual[y, 5e+19], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.60000000000000023e-4 or 5e19 < y

   1. Initial program 96.6%

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

   2. Taylor expanded in b around inf 42.0%

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

      1. mul-1-neg 42.0%

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

      2. distribute-rgt-neg-out 42.0%

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

   4. Simplified 42.0%

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

   5. Taylor expanded in a around 0 9.1%

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

      1. mul-1-neg 9.1%

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

      2. unsub-neg 9.1%

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

   7. Simplified 9.1%

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

   8. Taylor expanded in a around inf 23.0%

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

      1. neg-mul-1 23.0%

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

      2. *-commutative 23.0%

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

      3. distribute-rgt-neg-in 23.0%

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

   10. Simplified 23.0%

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

   11. Taylor expanded in b around 0 23.0%

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

       1. mul-1-neg 23.0%

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

       2. *-commutative 23.0%

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

       3. *-commutative 23.0%

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

       4. *-commutative 23.0%

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

       5. associate-*r* 23.4%

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

       6. distribute-rgt-neg-in 23.4%

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

   13. Simplified 23.4%

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

   if -3.60000000000000023e-4 < y < -4.6000000000000001e-217 or 5.50000000000000035e-304 < y < 5e19

   1. Initial program 92.2%

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

   2. Taylor expanded in b around inf 73.0%

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

      1. mul-1-neg 73.0%

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

      2. distribute-rgt-neg-out 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in a around 0 33.5%

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

   if -4.6000000000000001e-217 < y < 5.50000000000000035e-304

   1. Initial program 91.1%

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

   2. Taylor expanded in t around inf 18.4%

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

      1. mul-1-neg 18.4%

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

      2. distribute-lft-neg-out 18.4%

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

      3. *-commutative 18.4%

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

   4. Simplified 18.4%

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

   5. Taylor expanded in y around 0 5.1%

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

      1. associate-*r* 5.1%

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

      2. mul-1-neg 5.1%

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

      3. *-commutative 5.1%

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

   7. Simplified 5.1%

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

      1. distribute-lft-neg-out 5.1%

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

      2. unsub-neg 5.1%

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

      3. add-sqr-sqrt 2.9%

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

      4. sqrt-unprod 8.6%

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

      5. sqr-neg 8.6%

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

      6. sqrt-unprod 2.2%

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

      7. add-sqr-sqrt 5.1%

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

      8. associate-*r* 5.0%

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

      9. add-sqr-sqrt 2.2%

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

      10. sqrt-unprod 17.9%

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

      11. sqr-neg 17.9%

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

      12. sqrt-unprod 3.0%

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

      13. add-sqr-sqrt 5.1%

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

   9. Applied egg-rr 5.1%

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

   10. Taylor expanded in t around inf 32.6%

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

       1. *-commutative 32.6%

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

       2. associate-*r* 34.0%

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

       3. neg-mul-1 34.0%

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

       4. distribute-rgt-neg-in 34.0%

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

       5. distribute-rgt-neg-in 34.0%

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

   12. Simplified 34.0%

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

4. Final simplification 28.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00036:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-304}:\\ \;\;\;\;-x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 9: 23.3% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* x (- a)))))
   (if (<= a -6.8e-40)
     t_1
     (if (<= a 1.35e-291)
       x
       (if (<= a 9.5e-191) t_1 (if (<= a 5.1e+42) x (* y (* x (- t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (x * -a);
	double tmp;
	if (a <= -6.8e-40) {
		tmp = t_1;
	} else if (a <= 1.35e-291) {
		tmp = x;
	} else if (a <= 9.5e-191) {
		tmp = t_1;
	} else if (a <= 5.1e+42) {
		tmp = x;
	} else {
		tmp = y * (x * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (x * -a)
    if (a <= (-6.8d-40)) then
        tmp = t_1
    else if (a <= 1.35d-291) then
        tmp = x
    else if (a <= 9.5d-191) then
        tmp = t_1
    else if (a <= 5.1d+42) then
        tmp = x
    else
        tmp = y * (x * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (x * -a);
	double tmp;
	if (a <= -6.8e-40) {
		tmp = t_1;
	} else if (a <= 1.35e-291) {
		tmp = x;
	} else if (a <= 9.5e-191) {
		tmp = t_1;
	} else if (a <= 5.1e+42) {
		tmp = x;
	} else {
		tmp = y * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (x * -a)
	tmp = 0
	if a <= -6.8e-40:
		tmp = t_1
	elif a <= 1.35e-291:
		tmp = x
	elif a <= 9.5e-191:
		tmp = t_1
	elif a <= 5.1e+42:
		tmp = x
	else:
		tmp = y * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(x * Float64(-a)))
	tmp = 0.0
	if (a <= -6.8e-40)
		tmp = t_1;
	elseif (a <= 1.35e-291)
		tmp = x;
	elseif (a <= 9.5e-191)
		tmp = t_1;
	elseif (a <= 5.1e+42)
		tmp = x;
	else
		tmp = Float64(y * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (x * -a);
	tmp = 0.0;
	if (a <= -6.8e-40)
		tmp = t_1;
	elseif (a <= 1.35e-291)
		tmp = x;
	elseif (a <= 9.5e-191)
		tmp = t_1;
	elseif (a <= 5.1e+42)
		tmp = x;
	else
		tmp = y * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.8e-40], t$95$1, If[LessEqual[a, 1.35e-291], x, If[LessEqual[a, 9.5e-191], t$95$1, If[LessEqual[a, 5.1e+42], x, N[(y * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.79999999999999968e-40 or 1.34999999999999996e-291 < a < 9.4999999999999996e-191

   1. Initial program 88.1%

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

   2. Taylor expanded in b around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. distribute-rgt-neg-out 50.1%

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

   4. Simplified 50.1%

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

   5. Taylor expanded in a around 0 13.4%

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

      1. mul-1-neg 13.4%

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

      2. unsub-neg 13.4%

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

   7. Simplified 13.4%

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

   8. Taylor expanded in a around inf 21.8%

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

      1. neg-mul-1 21.8%

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

      2. *-commutative 21.8%

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

      3. distribute-rgt-neg-in 21.8%

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

   10. Simplified 21.8%

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

   11. Taylor expanded in b around 0 21.8%

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

       1. mul-1-neg 21.8%

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

       2. *-commutative 21.8%

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

       3. *-commutative 21.8%

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

       4. *-commutative 21.8%

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

       5. associate-*r* 24.2%

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

       6. distribute-rgt-neg-in 24.2%

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

   13. Simplified 24.2%

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

   if -6.79999999999999968e-40 < a < 1.34999999999999996e-291 or 9.4999999999999996e-191 < a < 5.0999999999999999e42

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. distribute-rgt-neg-out 58.2%

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

   4. Simplified 58.2%

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

   5. Taylor expanded in a around 0 28.1%

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

   if 5.0999999999999999e42 < a

   1. Initial program 91.9%

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

   2. Taylor expanded in t around inf 39.3%

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

      1. mul-1-neg 39.3%

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

      2. distribute-lft-neg-out 39.3%

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

      3. *-commutative 39.3%

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

   4. Simplified 39.3%

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

   5. Taylor expanded in y around 0 18.1%

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

      1. associate-*r* 18.1%

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

      2. mul-1-neg 18.1%

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

      3. *-commutative 18.1%

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

   7. Simplified 18.1%

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

      1. distribute-lft-neg-out 18.1%

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

      2. unsub-neg 18.1%

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

      3. add-sqr-sqrt 7.6%

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

      4. sqrt-unprod 13.1%

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

      5. sqr-neg 13.1%

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

      6. sqrt-unprod 5.9%

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

      7. add-sqr-sqrt 8.7%

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

      8. associate-*r* 8.7%

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

      9. add-sqr-sqrt 5.9%

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

      10. sqrt-unprod 13.2%

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

      11. sqr-neg 13.2%

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

      12. sqrt-unprod 7.6%

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

      13. add-sqr-sqrt 18.1%

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

   9. Applied egg-rr 18.1%

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

   10. Taylor expanded in t around inf 26.1%

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

       1. mul-1-neg 26.1%

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

       2. associate-*r* 26.0%

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

       3. *-commutative 26.0%

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

       4. *-commutative 26.0%

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

       5. distribute-rgt-neg-in 26.0%

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

   12. Simplified 26.0%

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

4. Final simplification 26.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-191}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 10: 23.9% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00042:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-304}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 34000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -0.00042)
   (* b (* x (- a)))
   (if (<= y -8.5e-159)
     x
     (if (<= y 5.5e-304)
       (* (- t) (* x y))
       (if (<= y 34000000000.0) x (* a (* x (- b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -0.00042) {
		tmp = b * (x * -a);
	} else if (y <= -8.5e-159) {
		tmp = x;
	} else if (y <= 5.5e-304) {
		tmp = -t * (x * y);
	} else if (y <= 34000000000.0) {
		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 <= (-0.00042d0)) then
        tmp = b * (x * -a)
    else if (y <= (-8.5d-159)) then
        tmp = x
    else if (y <= 5.5d-304) then
        tmp = -t * (x * y)
    else if (y <= 34000000000.0d0) 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 <= -0.00042) {
		tmp = b * (x * -a);
	} else if (y <= -8.5e-159) {
		tmp = x;
	} else if (y <= 5.5e-304) {
		tmp = -t * (x * y);
	} else if (y <= 34000000000.0) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -0.00042:
		tmp = b * (x * -a)
	elif y <= -8.5e-159:
		tmp = x
	elif y <= 5.5e-304:
		tmp = -t * (x * y)
	elif y <= 34000000000.0:
		tmp = x
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -0.00042)
		tmp = Float64(b * Float64(x * Float64(-a)));
	elseif (y <= -8.5e-159)
		tmp = x;
	elseif (y <= 5.5e-304)
		tmp = Float64(Float64(-t) * Float64(x * y));
	elseif (y <= 34000000000.0)
		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 <= -0.00042)
		tmp = b * (x * -a);
	elseif (y <= -8.5e-159)
		tmp = x;
	elseif (y <= 5.5e-304)
		tmp = -t * (x * y);
	elseif (y <= 34000000000.0)
		tmp = x;
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -0.00042], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e-159], x, If[LessEqual[y, 5.5e-304], N[((-t) * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 34000000000.0], x, N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2000000000000002e-4

   1. Initial program 98.2%

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

   2. Taylor expanded in b around inf 43.8%

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

      1. mul-1-neg 43.8%

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

      2. distribute-rgt-neg-out 43.8%

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

   4. Simplified 43.8%

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

   5. Taylor expanded in a around 0 10.4%

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

      1. mul-1-neg 10.4%

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

      2. unsub-neg 10.4%

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

   7. Simplified 10.4%

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

   8. Taylor expanded in a around inf 13.2%

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

      1. neg-mul-1 13.2%

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

      2. *-commutative 13.2%

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

      3. distribute-rgt-neg-in 13.2%

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

   10. Simplified 13.2%

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

   11. Taylor expanded in b around 0 13.2%

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

       1. mul-1-neg 13.2%

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

       2. *-commutative 13.2%

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

       3. *-commutative 13.2%

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

       4. *-commutative 13.2%

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

       5. associate-*r* 18.3%

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

       6. distribute-rgt-neg-in 18.3%

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

   13. Simplified 18.3%

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

   if -4.2000000000000002e-4 < y < -8.4999999999999998e-159 or 5.50000000000000035e-304 < y < 3.4e10

   1. Initial program 93.0%

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

   2. Taylor expanded in b around inf 76.5%

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

      1. mul-1-neg 76.5%

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

      2. distribute-rgt-neg-out 76.5%

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

   4. Simplified 76.5%

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

   5. Taylor expanded in a around 0 35.0%

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

   if -8.4999999999999998e-159 < y < 5.50000000000000035e-304

   1. Initial program 91.4%

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

   2. Taylor expanded in t around inf 32.9%

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

      1. mul-1-neg 32.9%

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

      2. distribute-lft-neg-out 32.9%

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

      3. *-commutative 32.9%

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

   4. Simplified 32.9%

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

   5. Taylor expanded in y around 0 13.2%

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

      1. associate-*r* 13.2%

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

      2. mul-1-neg 13.2%

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

      3. *-commutative 13.2%

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

   7. Simplified 13.2%

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

      1. distribute-lft-neg-out 13.2%

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

      2. unsub-neg 13.2%

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

      3. add-sqr-sqrt 5.1%

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

      4. sqrt-unprod 17.7%

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

      5. sqr-neg 17.7%

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

      6. sqrt-unprod 8.2%

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

      7. add-sqr-sqrt 13.3%

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

      8. associate-*r* 13.0%

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

      9. add-sqr-sqrt 8.0%

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

      10. sqrt-unprod 26.8%

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

      11. sqr-neg 26.8%

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

      12. sqrt-unprod 5.1%

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

      13. add-sqr-sqrt 12.9%

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

   9. Applied egg-rr 12.9%

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

   10. Taylor expanded in t around inf 33.4%

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

   if 3.4e10 < y

   1. Initial program 94.0%

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

   2. Taylor expanded in b around inf 38.8%

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

      1. mul-1-neg 38.8%

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

      2. distribute-rgt-neg-out 38.8%

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

   4. Simplified 38.8%

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

   5. Taylor expanded in a around 0 7.8%

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

      1. mul-1-neg 7.8%

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

      2. unsub-neg 7.8%

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

   7. Simplified 7.8%

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

   8. Taylor expanded in a around inf 31.7%

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

      1. neg-mul-1 31.7%

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

      2. *-commutative 31.7%

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

      3. distribute-rgt-neg-in 31.7%

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

   10. Simplified 31.7%

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

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00042:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-304}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 34000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 11: 33.1% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{-304} \lor \neg \left(y \leq 2.4 \cdot 10^{-62}\right):\\ \;\;\;\;\left(x \cdot \left(z \cdot z\right)\right) \cdot \left(a \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y 6e-304) (not (<= y 2.4e-62)))
   (* (* x (* z z)) (* a -0.5))
   (- x (* a (* x b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= 6e-304) || !(y <= 2.4e-62)) {
		tmp = (x * (z * z)) * (a * -0.5);
	} else {
		tmp = x - (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 <= 6d-304) .or. (.not. (y <= 2.4d-62))) then
        tmp = (x * (z * z)) * (a * (-0.5d0))
    else
        tmp = x - (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 <= 6e-304) || !(y <= 2.4e-62)) {
		tmp = (x * (z * z)) * (a * -0.5);
	} else {
		tmp = x - (a * (x * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= 6e-304) or not (y <= 2.4e-62):
		tmp = (x * (z * z)) * (a * -0.5)
	else:
		tmp = x - (a * (x * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= 6e-304) || !(y <= 2.4e-62))
		tmp = Float64(Float64(x * Float64(z * z)) * Float64(a * -0.5));
	else
		tmp = Float64(x - Float64(a * Float64(x * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= 6e-304) || ~((y <= 2.4e-62)))
		tmp = (x * (z * z)) * (a * -0.5);
	else
		tmp = x - (a * (x * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, 6e-304], N[Not[LessEqual[y, 2.4e-62]], $MachinePrecision]], N[(N[(x * N[(z * z), $MachinePrecision]), $MachinePrecision] * N[(a * -0.5), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.0000000000000002e-304 or 2.39999999999999984e-62 < y

   1. Initial program 94.9%

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

   2. Taylor expanded in y around 0 53.2%

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

      1. sub-neg 53.2%

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

      2. neg-mul-1 53.2%

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

      3. log1p-def 60.5%

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

      4. neg-mul-1 60.5%

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

   4. Simplified 60.5%

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

   5. Taylor expanded in a around 0 15.2%

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

      1. +-commutative 15.2%

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

      2. associate-*r* 15.6%

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

      3. fma-def 15.6%

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

      4. sub-neg 15.6%

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

      5. log1p-def 17.2%

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

   7. Simplified 17.2%

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

   8. Taylor expanded in z around 0 16.7%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(a \cdot \left(b \cdot x\right)\right) + \left(-1 \cdot \left(a \cdot \left(x \cdot z\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right)\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 16.7%

         \[\leadsto x + \left(\color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} + \left(-1 \cdot \left(a \cdot \left(x \cdot z\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right)\right) \]

      2. associate-+r+ 16.7%

         \[\leadsto x + \color{blue}{\left(\left(\left(-a \cdot \left(b \cdot x\right)\right) + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right)} \]

      3. neg-mul-1 16.7%

         \[\leadsto x + \left(\left(\color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      4. distribute-lft-out 16.7%

         \[\leadsto x + \left(\color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right) + a \cdot \left(x \cdot z\right)\right)} + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      5. distribute-lft-in 17.2%

         \[\leadsto x + \left(-1 \cdot \color{blue}{\left(a \cdot \left(b \cdot x + x \cdot z\right)\right)} + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      6. *-commutative 17.2%

         \[\leadsto x + \left(-1 \cdot \left(a \cdot \left(\color{blue}{x \cdot b} + x \cdot z\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      7. distribute-lft-in 17.2%

         \[\leadsto x + \left(-1 \cdot \left(a \cdot \color{blue}{\left(x \cdot \left(b + z\right)\right)}\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      8. associate-+r+ 17.2%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(a \cdot \left(x \cdot \left(b + z\right)\right)\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)} \]

   10. Simplified 17.2%

       \[\leadsto \color{blue}{\left(x - \left(b + z\right) \cdot \left(a \cdot x\right)\right) + -0.5 \cdot \left(x \cdot \left(a \cdot \left(z \cdot z\right)\right)\right)} \]

   11. Taylor expanded in z around inf 39.2%

       \[\leadsto \color{blue}{-0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 39.2%

          \[\leadsto \color{blue}{\left(-0.5 \cdot a\right) \cdot \left(x \cdot {z}^{2}\right)} \]

       2. *-commutative 39.2%

          \[\leadsto \color{blue}{\left(x \cdot {z}^{2}\right) \cdot \left(-0.5 \cdot a\right)} \]

       3. unpow2 39.2%

          \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot z\right)}\right) \cdot \left(-0.5 \cdot a\right) \]

       4. *-commutative 39.2%

          \[\leadsto \left(x \cdot \left(z \cdot z\right)\right) \cdot \color{blue}{\left(a \cdot -0.5\right)} \]

   13. Simplified 39.2%

       \[\leadsto \color{blue}{\left(x \cdot \left(z \cdot z\right)\right) \cdot \left(a \cdot -0.5\right)} \]

   if 6.0000000000000002e-304 < y < 2.39999999999999984e-62

   1. Initial program 91.6%

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

   2. Taylor expanded in b around inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-out 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in a around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. unsub-neg 51.5%

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

   7. Simplified 51.5%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{-304} \lor \neg \left(y \leq 2.4 \cdot 10^{-62}\right):\\ \;\;\;\;\left(x \cdot \left(z \cdot z\right)\right) \cdot \left(a \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \]

Alternative 12: 33.6% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{-304} \lor \neg \left(y \leq 1.1 \cdot 10^{-49}\right):\\ \;\;\;\;\left(x \cdot \left(z \cdot z\right)\right) \cdot \left(a \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(z + b\right) \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y 5.6e-304) (not (<= y 1.1e-49)))
   (* (* x (* z z)) (* a -0.5))
   (- x (* (+ z b) (* x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= 5.6e-304) || !(y <= 1.1e-49)) {
		tmp = (x * (z * z)) * (a * -0.5);
	} else {
		tmp = x - ((z + b) * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= 5.6d-304) .or. (.not. (y <= 1.1d-49))) then
        tmp = (x * (z * z)) * (a * (-0.5d0))
    else
        tmp = x - ((z + b) * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= 5.6e-304) || !(y <= 1.1e-49)) {
		tmp = (x * (z * z)) * (a * -0.5);
	} else {
		tmp = x - ((z + b) * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= 5.6e-304) or not (y <= 1.1e-49):
		tmp = (x * (z * z)) * (a * -0.5)
	else:
		tmp = x - ((z + b) * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= 5.6e-304) || !(y <= 1.1e-49))
		tmp = Float64(Float64(x * Float64(z * z)) * Float64(a * -0.5));
	else
		tmp = Float64(x - Float64(Float64(z + b) * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= 5.6e-304) || ~((y <= 1.1e-49)))
		tmp = (x * (z * z)) * (a * -0.5);
	else
		tmp = x - ((z + b) * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, 5.6e-304], N[Not[LessEqual[y, 1.1e-49]], $MachinePrecision]], N[(N[(x * N[(z * z), $MachinePrecision]), $MachinePrecision] * N[(a * -0.5), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z + b), $MachinePrecision] * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.5999999999999997e-304 or 1.09999999999999995e-49 < y

   1. Initial program 94.9%

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

   2. Taylor expanded in y around 0 53.1%

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

      1. sub-neg 53.1%

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

      2. neg-mul-1 53.1%

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

      3. log1p-def 60.5%

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

      4. neg-mul-1 60.5%

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

   4. Simplified 60.5%

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

   5. Taylor expanded in a around 0 14.6%

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

      1. +-commutative 14.6%

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

      2. associate-*r* 15.1%

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

      3. fma-def 15.1%

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

      4. sub-neg 15.1%

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

      5. log1p-def 16.6%

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

   7. Simplified 16.6%

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

   8. Taylor expanded in z around 0 16.0%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(a \cdot \left(b \cdot x\right)\right) + \left(-1 \cdot \left(a \cdot \left(x \cdot z\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right)\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 16.0%

         \[\leadsto x + \left(\color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} + \left(-1 \cdot \left(a \cdot \left(x \cdot z\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right)\right) \]

      2. associate-+r+ 16.0%

         \[\leadsto x + \color{blue}{\left(\left(\left(-a \cdot \left(b \cdot x\right)\right) + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right)} \]

      3. neg-mul-1 16.0%

         \[\leadsto x + \left(\left(\color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      4. distribute-lft-out 16.0%

         \[\leadsto x + \left(\color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right) + a \cdot \left(x \cdot z\right)\right)} + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      5. distribute-lft-in 16.6%

         \[\leadsto x + \left(-1 \cdot \color{blue}{\left(a \cdot \left(b \cdot x + x \cdot z\right)\right)} + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      6. *-commutative 16.6%

         \[\leadsto x + \left(-1 \cdot \left(a \cdot \left(\color{blue}{x \cdot b} + x \cdot z\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      7. distribute-lft-in 16.6%

         \[\leadsto x + \left(-1 \cdot \left(a \cdot \color{blue}{\left(x \cdot \left(b + z\right)\right)}\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      8. associate-+r+ 16.6%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(a \cdot \left(x \cdot \left(b + z\right)\right)\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)} \]

   10. Simplified 16.6%

       \[\leadsto \color{blue}{\left(x - \left(b + z\right) \cdot \left(a \cdot x\right)\right) + -0.5 \cdot \left(x \cdot \left(a \cdot \left(z \cdot z\right)\right)\right)} \]

   11. Taylor expanded in z around inf 39.2%

       \[\leadsto \color{blue}{-0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 39.2%

          \[\leadsto \color{blue}{\left(-0.5 \cdot a\right) \cdot \left(x \cdot {z}^{2}\right)} \]

       2. *-commutative 39.2%

          \[\leadsto \color{blue}{\left(x \cdot {z}^{2}\right) \cdot \left(-0.5 \cdot a\right)} \]

       3. unpow2 39.2%

          \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot z\right)}\right) \cdot \left(-0.5 \cdot a\right) \]

       4. *-commutative 39.2%

          \[\leadsto \left(x \cdot \left(z \cdot z\right)\right) \cdot \color{blue}{\left(a \cdot -0.5\right)} \]

   13. Simplified 39.2%

       \[\leadsto \color{blue}{\left(x \cdot \left(z \cdot z\right)\right) \cdot \left(a \cdot -0.5\right)} \]

   if 5.5999999999999997e-304 < y < 1.09999999999999995e-49

   1. Initial program 91.8%

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

   2. Taylor expanded in y around 0 81.2%

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

      1. sub-neg 81.2%

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

      2. neg-mul-1 81.2%

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

      3. log1p-def 89.4%

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

      4. neg-mul-1 89.4%

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

   4. Simplified 89.4%

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

   5. Taylor expanded in z around 0 89.4%

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

      1. associate-*r* 89.4%

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

      2. neg-mul-1 89.4%

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

      3. associate-*r* 89.4%

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

      4. neg-mul-1 89.4%

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

      5. distribute-lft-out 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in a around 0 53.9%

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

      1. mul-1-neg 53.9%

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

      2. unsub-neg 53.9%

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

      3. *-commutative 53.9%

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

      4. *-commutative 53.9%

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

      5. associate-*l* 53.8%

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

      6. *-commutative 53.8%

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

   10. Simplified 53.8%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{-304} \lor \neg \left(y \leq 1.1 \cdot 10^{-49}\right):\\ \;\;\;\;\left(x \cdot \left(z \cdot z\right)\right) \cdot \left(a \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(z + b\right) \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 13: 26.6% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0019 \lor \neg \left(y \leq 5 \cdot 10^{+19}\right):\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.0019) (not (<= y 5e+19))) (* b (* x (- a))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.0019) || !(y <= 5e+19)) {
		tmp = b * (x * -a);
	} 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 <= (-0.0019d0)) .or. (.not. (y <= 5d+19))) then
        tmp = b * (x * -a)
    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 <= -0.0019) || !(y <= 5e+19)) {
		tmp = b * (x * -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -0.0019) or not (y <= 5e+19):
		tmp = b * (x * -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -0.0019) || !(y <= 5e+19))
		tmp = Float64(b * Float64(x * Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -0.0019) || ~((y <= 5e+19)))
		tmp = b * (x * -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -0.0019], N[Not[LessEqual[y, 5e+19]], $MachinePrecision]], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -0.0019 or 5e19 < y

   1. Initial program 96.6%

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

   2. Taylor expanded in b around inf 42.0%

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

      1. mul-1-neg 42.0%

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

      2. distribute-rgt-neg-out 42.0%

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

   4. Simplified 42.0%

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

   5. Taylor expanded in a around 0 9.1%

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

      1. mul-1-neg 9.1%

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

      2. unsub-neg 9.1%

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

   7. Simplified 9.1%

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

   8. Taylor expanded in a around inf 23.0%

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

      1. neg-mul-1 23.0%

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

      2. *-commutative 23.0%

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

      3. distribute-rgt-neg-in 23.0%

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

   10. Simplified 23.0%

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

   11. Taylor expanded in b around 0 23.0%

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

       1. mul-1-neg 23.0%

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

       2. *-commutative 23.0%

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

       3. *-commutative 23.0%

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

       4. *-commutative 23.0%

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

       5. associate-*r* 23.4%

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

       6. distribute-rgt-neg-in 23.4%

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

   13. Simplified 23.4%

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

   if -0.0019 < y < 5e19

   1. Initial program 92.0%

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

   2. Taylor expanded in b around inf 73.0%

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

      1. mul-1-neg 73.0%

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

      2. distribute-rgt-neg-out 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in a around 0 29.0%

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

4. Final simplification 26.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0019 \lor \neg \left(y \leq 5 \cdot 10^{+19}\right):\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 19.1% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-94}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-x \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.2e-137)
   x
   (if (<= x 1.7e-94) (* a (* x (- b))) (- (* x (* y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.2e-137) {
		tmp = x;
	} else if (x <= 1.7e-94) {
		tmp = a * (x * -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 (x <= (-2.2d-137)) then
        tmp = x
    else if (x <= 1.7d-94) then
        tmp = a * (x * -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 (x <= -2.2e-137) {
		tmp = x;
	} else if (x <= 1.7e-94) {
		tmp = a * (x * -b);
	} else {
		tmp = -(x * (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.2e-137:
		tmp = x
	elif x <= 1.7e-94:
		tmp = a * (x * -b)
	else:
		tmp = -(x * (y * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.2e-137)
		tmp = x;
	elseif (x <= 1.7e-94)
		tmp = Float64(a * Float64(x * Float64(-b)));
	else
		tmp = Float64(-Float64(x * Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.2e-137)
		tmp = x;
	elseif (x <= 1.7e-94)
		tmp = a * (x * -b);
	else
		tmp = -(x * (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.2e-137], x, If[LessEqual[x, 1.7e-94], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], (-N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2000000000000001e-137

   1. Initial program 93.2%

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

   2. Taylor expanded in b around inf 61.8%

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

      1. mul-1-neg 61.8%

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

      2. distribute-rgt-neg-out 61.8%

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

   4. Simplified 61.8%

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

   5. Taylor expanded in a around 0 21.7%

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

   if -2.2000000000000001e-137 < x < 1.6999999999999999e-94

   1. Initial program 97.6%

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

   2. Taylor expanded in b around inf 56.1%

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

      1. mul-1-neg 56.1%

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

      2. distribute-rgt-neg-out 56.1%

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

   4. Simplified 56.1%

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

   5. Taylor expanded in a around 0 17.8%

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

      1. mul-1-neg 17.8%

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

      2. unsub-neg 17.8%

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

   7. Simplified 17.8%

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

   8. Taylor expanded in a around inf 33.4%

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

      1. neg-mul-1 33.4%

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

      2. *-commutative 33.4%

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

      3. distribute-rgt-neg-in 33.4%

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

   10. Simplified 33.4%

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

   if 1.6999999999999999e-94 < x

   1. Initial program 92.0%

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

   2. Taylor expanded in t around inf 59.5%

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

      1. mul-1-neg 59.5%

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

      2. distribute-lft-neg-out 59.5%

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

      3. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in y around 0 25.6%

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

      1. associate-*r* 25.6%

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

      2. mul-1-neg 25.6%

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

      3. *-commutative 25.6%

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

   7. Simplified 25.6%

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

      1. distribute-lft-neg-out 25.6%

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

      2. unsub-neg 25.6%

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

      3. add-sqr-sqrt 8.5%

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

      4. sqrt-unprod 20.3%

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

      5. sqr-neg 20.3%

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

      6. sqrt-unprod 9.8%

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

      7. add-sqr-sqrt 13.5%

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

      8. associate-*r* 13.5%

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

      9. add-sqr-sqrt 9.8%

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

      10. sqrt-unprod 19.3%

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

      11. sqr-neg 19.3%

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

      12. sqrt-unprod 7.5%

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

      13. add-sqr-sqrt 23.4%

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

   9. Applied egg-rr 23.4%

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

   10. Taylor expanded in t around inf 19.5%

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

       1. *-commutative 19.5%

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

       2. associate-*r* 18.8%

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

       3. neg-mul-1 18.8%

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

       4. distribute-rgt-neg-in 18.8%

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

       5. distribute-rgt-neg-in 18.8%

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

   12. Simplified 18.8%

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

4. Final simplification 24.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-94}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-x \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 15: 31.4% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 34000000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 34000000000.0) (* x (- 1.0 (* a b))) (* a (* x (- b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 34000000000.0) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 34000000000.0d0) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 34000000000.0) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 34000000000.0:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 34000000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 34000000000.0)
		tmp = x * (1.0 - (a * b));
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 34000000000.0], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.4e10

   1. Initial program 94.2%

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

   2. Taylor expanded in b around inf 65.7%

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

      1. mul-1-neg 65.7%

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

      2. distribute-rgt-neg-out 65.7%

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

   4. Simplified 65.7%

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

   5. Taylor expanded in a around 0 27.6%

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

      1. mul-1-neg 27.6%

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

      2. unsub-neg 27.6%

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

   7. Simplified 27.6%

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

   8. Taylor expanded in x around 0 29.0%

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

   if 3.4e10 < y

   1. Initial program 94.0%

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

   2. Taylor expanded in b around inf 38.8%

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

      1. mul-1-neg 38.8%

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

      2. distribute-rgt-neg-out 38.8%

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

   4. Simplified 38.8%

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

   5. Taylor expanded in a around 0 7.8%

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

      1. mul-1-neg 7.8%

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

      2. unsub-neg 7.8%

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

   7. Simplified 7.8%

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

   8. Taylor expanded in a around inf 31.7%

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

      1. neg-mul-1 31.7%

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

      2. *-commutative 31.7%

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

      3. distribute-rgt-neg-in 31.7%

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

   10. Simplified 31.7%

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

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 34000000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 16: 31.4% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 35000000000:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 35000000000.0) (- x (* x (* a b))) (* a (* x (- b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 35000000000.0) {
		tmp = x - (x * (a * b));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 35000000000.0d0) then
        tmp = x - (x * (a * b))
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 35000000000.0) {
		tmp = x - (x * (a * b));
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 35000000000.0:
		tmp = x - (x * (a * b))
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 35000000000.0)
		tmp = Float64(x - Float64(x * Float64(a * b)));
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 35000000000.0)
		tmp = x - (x * (a * b));
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 35000000000.0], N[(x - N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.5e10

   1. Initial program 94.2%

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

   2. Taylor expanded in y around 0 67.2%

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

      1. sub-neg 67.2%

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

      2. neg-mul-1 67.2%

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

      3. log1p-def 75.9%

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

      4. neg-mul-1 75.9%

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

   4. Simplified 75.9%

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

   5. Taylor expanded in a around 0 28.6%

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

      1. +-commutative 28.6%

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

      2. associate-*r* 29.0%

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

      3. fma-def 29.0%

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

      4. sub-neg 29.0%

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

      5. log1p-def 31.2%

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

   7. Simplified 31.2%

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

   8. Taylor expanded in z around 0 30.2%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(a \cdot \left(b \cdot x\right)\right) + \left(-1 \cdot \left(a \cdot \left(x \cdot z\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right)\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 30.2%

         \[\leadsto x + \left(\color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} + \left(-1 \cdot \left(a \cdot \left(x \cdot z\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right)\right) \]

      2. associate-+r+ 30.2%

         \[\leadsto x + \color{blue}{\left(\left(\left(-a \cdot \left(b \cdot x\right)\right) + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right)} \]

      3. neg-mul-1 30.2%

         \[\leadsto x + \left(\left(\color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      4. distribute-lft-out 30.2%

         \[\leadsto x + \left(\color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right) + a \cdot \left(x \cdot z\right)\right)} + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      5. distribute-lft-in 31.3%

         \[\leadsto x + \left(-1 \cdot \color{blue}{\left(a \cdot \left(b \cdot x + x \cdot z\right)\right)} + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      6. *-commutative 31.3%

         \[\leadsto x + \left(-1 \cdot \left(a \cdot \left(\color{blue}{x \cdot b} + x \cdot z\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      7. distribute-lft-in 31.3%

         \[\leadsto x + \left(-1 \cdot \left(a \cdot \color{blue}{\left(x \cdot \left(b + z\right)\right)}\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)\right) \]

      8. associate-+r+ 31.3%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(a \cdot \left(x \cdot \left(b + z\right)\right)\right)\right) + -0.5 \cdot \left(a \cdot \left(x \cdot {z}^{2}\right)\right)} \]

   10. Simplified 31.2%

       \[\leadsto \color{blue}{\left(x - \left(b + z\right) \cdot \left(a \cdot x\right)\right) + -0.5 \cdot \left(x \cdot \left(a \cdot \left(z \cdot z\right)\right)\right)} \]

   11. Taylor expanded in z around 0 27.6%

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

       1. associate-*r* 29.0%

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

       2. *-commutative 29.0%

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

   13. Simplified 29.0%

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

   if 3.5e10 < y

   1. Initial program 94.0%

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

   2. Taylor expanded in b around inf 38.8%

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

      1. mul-1-neg 38.8%

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

      2. distribute-rgt-neg-out 38.8%

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

   4. Simplified 38.8%

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

   5. Taylor expanded in a around 0 7.8%

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

      1. mul-1-neg 7.8%

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

      2. unsub-neg 7.8%

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

   7. Simplified 7.8%

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

   8. Taylor expanded in a around inf 31.7%

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

      1. neg-mul-1 31.7%

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

      2. *-commutative 31.7%

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

      3. distribute-rgt-neg-in 31.7%

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

   10. Simplified 31.7%

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

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 35000000000:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 17: 19.1% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.2%

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

2. Taylor expanded in b around inf 58.7%

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

   1. mul-1-neg 58.7%

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

   2. distribute-rgt-neg-out 58.7%

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

4. Simplified 58.7%

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

5. Taylor expanded in a around 0 17.5%

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

6. Final simplification 17.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(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))))))