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

Percentage Accurate: 96.6% → 99.3%

Time: 23.2s

Alternatives: 16

Speedup: 1.5×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

2. Taylor expanded in z around 0 100.0%

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

   1. associate-*r* 100.0%

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

   2. associate-*r* 100.0%

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

   3. distribute-lft-out 100.0%

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

   4. neg-mul-1 100.0%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 87.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-11} \lor \neg \left(y \leq 1.35 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.65e-11) (not (<= y 1.35e+16)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* (- a) (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.65e-11) || !(y <= 1.35e+16)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((-a * (z + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.65d-11)) .or. (.not. (y <= 1.35d+16))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((-a * (z + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.65e-11) || !(y <= 1.35e+16)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((-a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.65e-11) or not (y <= 1.35e+16):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((-a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.65e-11) || !(y <= 1.35e+16))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.65e-11) || ~((y <= 1.35e+16)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((-a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.65e-11], N[Not[LessEqual[y, 1.35e+16]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6500000000000001e-11 or 1.35e16 < y

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 94.4%

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

   if -1.6500000000000001e-11 < y < 1.35e16

   1. Initial program 94.1%

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

   2. Taylor expanded in y around 0 84.8%

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

   3. Taylor expanded in z around 0 91.5%

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

      1. neg-mul-1 91.5%

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

   5. Simplified 91.5%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-11} \lor \neg \left(y \leq 1.35 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]

Alternative 3: 74.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+21}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+22}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.7e+21)
   (* x (pow z y))
   (if (<= y 1.25e+22) (* x (exp (* (- a) (+ z b)))) (* x (exp (* y (- t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.7e+21) {
		tmp = x * pow(z, y);
	} else if (y <= 1.25e+22) {
		tmp = x * exp((-a * (z + b)));
	} else {
		tmp = x * exp((y * -t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.7d+21)) then
        tmp = x * (z ** y)
    else if (y <= 1.25d+22) then
        tmp = x * exp((-a * (z + b)))
    else
        tmp = x * exp((y * -t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.7e+21) {
		tmp = x * Math.pow(z, y);
	} else if (y <= 1.25e+22) {
		tmp = x * Math.exp((-a * (z + b)));
	} else {
		tmp = x * Math.exp((y * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.7e+21:
		tmp = x * math.pow(z, y)
	elif y <= 1.25e+22:
		tmp = x * math.exp((-a * (z + b)))
	else:
		tmp = x * math.exp((y * -t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.7e+21)
		tmp = Float64(x * (z ^ y));
	elseif (y <= 1.25e+22)
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	else
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.7e+21)
		tmp = x * (z ^ y);
	elseif (y <= 1.25e+22)
		tmp = x * exp((-a * (z + b)));
	else
		tmp = x * exp((y * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.7e+21], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+22], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7e21

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 92.1%

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

   5. Taylor expanded in t around 0 71.4%

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

   6. Taylor expanded in x around 0 71.4%

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

   if -3.7e21 < y < 1.2499999999999999e22

   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 y around 0 82.2%

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

   3. Taylor expanded in z around 0 88.4%

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

      1. neg-mul-1 88.4%

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

   5. Simplified 88.4%

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

   if 1.2499999999999999e22 < y

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 98.6%

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

   5. Taylor expanded in t around inf 74.4%

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

      1. mul-1-neg 74.4%

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

      2. distribute-lft-neg-out 74.4%

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

      3. *-commutative 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+21}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+22}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 4: 73.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+23} \lor \neg \left(y \leq 1.35 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.2e+23) (not (<= y 1.35e+16)))
   (* x (pow z y))
   (* x (exp (* (- a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+23) || !(y <= 1.35e+16)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp((-a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.2d+23)) .or. (.not. (y <= 1.35d+16))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp((-a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+23) || !(y <= 1.35e+16)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((-a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.2e+23) or not (y <= 1.35e+16):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((-a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.2e+23) || !(y <= 1.35e+16))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(Float64(-a) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.2e+23) || ~((y <= 1.35e+16)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((-a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.2e+23], N[Not[LessEqual[y, 1.35e+16]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[((-a) * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e23 or 1.35e16 < y

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 94.9%

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

   5. Taylor expanded in t around 0 69.9%

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

   6. Taylor expanded in x around 0 69.9%

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

   if -3.2e23 < y < 1.35e16

   1. Initial program 94.4%

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

   2. Taylor expanded in y around 0 83.2%

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

   3. Taylor expanded in z around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. *-commutative 79.2%

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

      3. distribute-rgt-neg-in 79.2%

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

   5. Simplified 79.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+23} \lor \neg \left(y \leq 1.35 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot b}\\ \end{array} \]

Alternative 5: 71.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+20}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+21}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.45e+20)
   (* x (pow z y))
   (if (<= y 5.8e+21) (* x (exp (* (- a) b))) (* x (exp (* y (- t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.45e+20) {
		tmp = x * pow(z, y);
	} else if (y <= 5.8e+21) {
		tmp = x * exp((-a * b));
	} else {
		tmp = x * exp((y * -t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.45d+20)) then
        tmp = x * (z ** y)
    else if (y <= 5.8d+21) then
        tmp = x * exp((-a * b))
    else
        tmp = x * exp((y * -t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.45e+20) {
		tmp = x * Math.pow(z, y);
	} else if (y <= 5.8e+21) {
		tmp = x * Math.exp((-a * b));
	} else {
		tmp = x * Math.exp((y * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.45e+20:
		tmp = x * math.pow(z, y)
	elif y <= 5.8e+21:
		tmp = x * math.exp((-a * b))
	else:
		tmp = x * math.exp((y * -t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.45e+20)
		tmp = Float64(x * (z ^ y));
	elseif (y <= 5.8e+21)
		tmp = Float64(x * exp(Float64(Float64(-a) * b)));
	else
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.45e+20)
		tmp = x * (z ^ y);
	elseif (y <= 5.8e+21)
		tmp = x * exp((-a * b));
	else
		tmp = x * exp((y * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.45e+20], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+21], N[(x * N[Exp[N[((-a) * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e20

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 92.1%

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

   5. Taylor expanded in t around 0 71.4%

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

   6. Taylor expanded in x around 0 71.4%

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

   if -1.45e20 < y < 5.8e21

   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 y around 0 82.2%

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

   3. Taylor expanded in z around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. *-commutative 78.3%

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

      3. distribute-rgt-neg-in 78.3%

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

   5. Simplified 78.3%

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

   if 5.8e21 < y

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 98.6%

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

   5. Taylor expanded in t around inf 74.4%

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

      1. mul-1-neg 74.4%

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

      2. distribute-lft-neg-out 74.4%

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

      3. *-commutative 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+20}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+21}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 6: 55.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -900000000:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -900000000.0) (* x (- 1.0 (* y t))) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -900000000.0) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-900000000.0d0)) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -900000000.0) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -900000000.0:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -900000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -900000000.0)
		tmp = x * (1.0 - (y * t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -900000000.0], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9e8

   1. Initial program 98.6%

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

      1. fma-def 98.6%

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

      2. sub-neg 98.6%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 82.1%

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

   5. Taylor expanded in t around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. distribute-lft-neg-out 82.1%

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

      3. *-commutative 82.1%

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

   7. Simplified 82.1%

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

   8. Taylor expanded in y around 0 30.6%

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

      1. mul-1-neg 30.6%

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

      2. unsub-neg 30.6%

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

      3. *-commutative 30.6%

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

      4. associate-*l* 34.4%

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

      5. *-commutative 34.4%

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

   10. Simplified 34.4%

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

   11. Taylor expanded in x around 0 34.4%

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

   if -9e8 < t

   1. Initial program 96.8%

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

      1. fma-def 96.8%

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

      2. sub-neg 96.8%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 73.1%

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

   5. Taylor expanded in t around 0 68.4%

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

   6. Taylor expanded in x around 0 68.4%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -900000000:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 7: 29.7% accurate, 20.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-138} \lor \neg \left(x \leq 3.8 \cdot 10^{-210} \lor \neg \left(x \leq 4.8 \cdot 10^{-155}\right) \land x \leq 3\right):\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -9.8e-138)
         (not (or (<= x 3.8e-210) (and (not (<= x 4.8e-155)) (<= x 3.0)))))
   (* x (- 1.0 (* y t)))
   (* a (* x (- z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -9.8e-138) || !((x <= 3.8e-210) || (!(x <= 4.8e-155) && (x <= 3.0)))) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-9.8d-138)) .or. (.not. (x <= 3.8d-210) .or. (.not. (x <= 4.8d-155)) .and. (x <= 3.0d0))) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -9.8e-138) || !((x <= 3.8e-210) || (!(x <= 4.8e-155) && (x <= 3.0)))) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -9.8e-138) or not ((x <= 3.8e-210) or (not (x <= 4.8e-155) and (x <= 3.0))):
		tmp = x * (1.0 - (y * t))
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -9.8e-138) || !((x <= 3.8e-210) || (!(x <= 4.8e-155) && (x <= 3.0))))
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -9.8e-138) || ~(((x <= 3.8e-210) || (~((x <= 4.8e-155)) && (x <= 3.0)))))
		tmp = x * (1.0 - (y * t));
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -9.8e-138], N[Not[Or[LessEqual[x, 3.8e-210], And[N[Not[LessEqual[x, 4.8e-155]], $MachinePrecision], LessEqual[x, 3.0]]]], $MachinePrecision]], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.80000000000000033e-138 or 3.80000000000000003e-210 < x < 4.8e-155 or 3 < x

   1. Initial program 96.7%

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

      1. fma-def 96.7%

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

      2. sub-neg 96.7%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 75.2%

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

   5. Taylor expanded in t around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. distribute-lft-neg-out 63.2%

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

      3. *-commutative 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in y around 0 38.3%

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

      1. mul-1-neg 38.3%

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

      2. unsub-neg 38.3%

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

      3. *-commutative 38.3%

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

      4. associate-*l* 38.4%

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

      5. *-commutative 38.4%

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

   10. Simplified 38.4%

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

   11. Taylor expanded in x around 0 38.4%

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

   if -9.80000000000000033e-138 < x < 3.80000000000000003e-210 or 4.8e-155 < x < 3

   1. Initial program 98.8%

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

   2. Taylor expanded in y around 0 52.0%

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

   3. Taylor expanded in b around 0 11.9%

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

   4. Taylor expanded in z around 0 11.8%

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

      1. mul-1-neg 11.8%

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

      2. unsub-neg 11.8%

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

   6. Simplified 11.8%

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

   7. Taylor expanded in a around inf 35.7%

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

      1. mul-1-neg 35.7%

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

      2. *-commutative 35.7%

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

      3. distribute-rgt-neg-in 35.7%

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

   9. Simplified 35.7%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-138} \lor \neg \left(x \leq 3.8 \cdot 10^{-210} \lor \neg \left(x \leq 4.8 \cdot 10^{-155}\right) \land x \leq 3\right):\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 8: 29.6% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+184} \lor \neg \left(y \leq 4.5 \cdot 10^{+230}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* y (- t)))))
   (if (<= y -2.2e+23)
     t_1
     (if (<= y 3.7e-12)
       x
       (if (or (<= y 3.5e+184) (not (<= y 4.5e+230)))
         (* z (* x (- a)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y * -t);
	double tmp;
	if (y <= -2.2e+23) {
		tmp = t_1;
	} else if (y <= 3.7e-12) {
		tmp = x;
	} else if ((y <= 3.5e+184) || !(y <= 4.5e+230)) {
		tmp = z * (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 * (y * -t)
    if (y <= (-2.2d+23)) then
        tmp = t_1
    else if (y <= 3.7d-12) then
        tmp = x
    else if ((y <= 3.5d+184) .or. (.not. (y <= 4.5d+230))) then
        tmp = z * (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 * (y * -t);
	double tmp;
	if (y <= -2.2e+23) {
		tmp = t_1;
	} else if (y <= 3.7e-12) {
		tmp = x;
	} else if ((y <= 3.5e+184) || !(y <= 4.5e+230)) {
		tmp = z * (x * -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (y * -t)
	tmp = 0
	if y <= -2.2e+23:
		tmp = t_1
	elif y <= 3.7e-12:
		tmp = x
	elif (y <= 3.5e+184) or not (y <= 4.5e+230):
		tmp = z * (x * -a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(y * Float64(-t)))
	tmp = 0.0
	if (y <= -2.2e+23)
		tmp = t_1;
	elseif (y <= 3.7e-12)
		tmp = x;
	elseif ((y <= 3.5e+184) || !(y <= 4.5e+230))
		tmp = Float64(z * Float64(x * Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (y * -t);
	tmp = 0.0;
	if (y <= -2.2e+23)
		tmp = t_1;
	elseif (y <= 3.7e-12)
		tmp = x;
	elseif ((y <= 3.5e+184) || ~((y <= 4.5e+230)))
		tmp = z * (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[(y * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+23], t$95$1, If[LessEqual[y, 3.7e-12], x, If[Or[LessEqual[y, 3.5e+184], N[Not[LessEqual[y, 4.5e+230]], $MachinePrecision]], N[(z * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.20000000000000008e23 or 3.49999999999999978e184 < y < 4.4999999999999999e230

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 93.6%

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

   5. Taylor expanded in t around inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. distribute-lft-neg-out 64.8%

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

      3. *-commutative 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in y around 0 29.2%

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

      1. mul-1-neg 29.2%

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

      2. unsub-neg 29.2%

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

      3. *-commutative 29.2%

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

      4. associate-*l* 28.2%

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

      5. *-commutative 28.2%

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

   10. Simplified 28.2%

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

   11. Taylor expanded in t around inf 30.3%

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

       1. mul-1-neg 30.3%

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

       2. associate-*r* 25.4%

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

       3. *-commutative 25.4%

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

       4. distribute-rgt-neg-in 25.4%

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

       5. associate-*r* 29.1%

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

   13. Simplified 29.1%

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

   if -2.20000000000000008e23 < y < 3.69999999999999999e-12

   1. Initial program 95.0%

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

   2. Taylor expanded in y around 0 83.3%

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

   3. Taylor expanded in a around 0 35.6%

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

   if 3.69999999999999999e-12 < y < 3.49999999999999978e184 or 4.4999999999999999e230 < y

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 36.2%

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

   3. Taylor expanded in b around 0 5.4%

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

   4. Taylor expanded in z around 0 5.4%

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

      1. mul-1-neg 5.4%

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

      2. unsub-neg 5.4%

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

   6. Simplified 5.4%

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

   7. Taylor expanded in a around inf 31.4%

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

      1. mul-1-neg 31.4%

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

      2. associate-*r* 32.4%

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

   9. Simplified 32.4%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+184} \lor \neg \left(y \leq 4.5 \cdot 10^{+230}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 9: 29.6% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+185}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+230}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* y (- t)))))
   (if (<= y -3e+22)
     t_1
     (if (<= y 2.6e-16)
       x
       (if (<= y 4e+185)
         (* z (* x (- a)))
         (if (<= y 4.2e+230) t_1 (* a (* x (- z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y * -t);
	double tmp;
	if (y <= -3e+22) {
		tmp = t_1;
	} else if (y <= 2.6e-16) {
		tmp = x;
	} else if (y <= 4e+185) {
		tmp = z * (x * -a);
	} else if (y <= 4.2e+230) {
		tmp = t_1;
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * -t)
    if (y <= (-3d+22)) then
        tmp = t_1
    else if (y <= 2.6d-16) then
        tmp = x
    else if (y <= 4d+185) then
        tmp = z * (x * -a)
    else if (y <= 4.2d+230) then
        tmp = t_1
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y * -t);
	double tmp;
	if (y <= -3e+22) {
		tmp = t_1;
	} else if (y <= 2.6e-16) {
		tmp = x;
	} else if (y <= 4e+185) {
		tmp = z * (x * -a);
	} else if (y <= 4.2e+230) {
		tmp = t_1;
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (y * -t)
	tmp = 0
	if y <= -3e+22:
		tmp = t_1
	elif y <= 2.6e-16:
		tmp = x
	elif y <= 4e+185:
		tmp = z * (x * -a)
	elif y <= 4.2e+230:
		tmp = t_1
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(y * Float64(-t)))
	tmp = 0.0
	if (y <= -3e+22)
		tmp = t_1;
	elseif (y <= 2.6e-16)
		tmp = x;
	elseif (y <= 4e+185)
		tmp = Float64(z * Float64(x * Float64(-a)));
	elseif (y <= 4.2e+230)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (y * -t);
	tmp = 0.0;
	if (y <= -3e+22)
		tmp = t_1;
	elseif (y <= 2.6e-16)
		tmp = x;
	elseif (y <= 4e+185)
		tmp = z * (x * -a);
	elseif (y <= 4.2e+230)
		tmp = t_1;
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e+22], t$95$1, If[LessEqual[y, 2.6e-16], x, If[LessEqual[y, 4e+185], N[(z * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+230], t$95$1, N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3e22 or 3.9999999999999999e185 < y < 4.19999999999999986e230

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 93.6%

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

   5. Taylor expanded in t around inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. distribute-lft-neg-out 64.8%

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

      3. *-commutative 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in y around 0 29.2%

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

      1. mul-1-neg 29.2%

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

      2. unsub-neg 29.2%

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

      3. *-commutative 29.2%

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

      4. associate-*l* 28.2%

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

      5. *-commutative 28.2%

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

   10. Simplified 28.2%

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

   11. Taylor expanded in t around inf 30.3%

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

       1. mul-1-neg 30.3%

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

       2. associate-*r* 25.4%

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

       3. *-commutative 25.4%

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

       4. distribute-rgt-neg-in 25.4%

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

       5. associate-*r* 29.1%

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

   13. Simplified 29.1%

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

   if -3e22 < y < 2.5999999999999998e-16

   1. Initial program 95.0%

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

   2. Taylor expanded in y around 0 83.3%

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

   3. Taylor expanded in a around 0 35.6%

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

   if 2.5999999999999998e-16 < y < 3.9999999999999999e185

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 40.5%

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

   3. Taylor expanded in b around 0 6.1%

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

   4. Taylor expanded in z around 0 6.2%

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

      1. mul-1-neg 6.2%

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

      2. unsub-neg 6.2%

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

   6. Simplified 6.2%

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

   7. Taylor expanded in a around inf 30.9%

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

      1. mul-1-neg 30.9%

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

      2. associate-*r* 33.0%

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

   9. Simplified 33.0%

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

   if 4.19999999999999986e230 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 27.3%

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

   3. Taylor expanded in b around 0 3.8%

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

   4. Taylor expanded in z around 0 3.8%

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

      1. mul-1-neg 3.8%

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

      2. unsub-neg 3.8%

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

   6. Simplified 3.8%

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

   7. Taylor expanded in a around inf 32.3%

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

      1. mul-1-neg 32.3%

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

      2. *-commutative 32.3%

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

      3. distribute-rgt-neg-in 32.3%

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

   9. Simplified 32.3%

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

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+185}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 10: 29.6% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+181}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.5e+19)
   (* t (* x (- y)))
   (if (<= y 2.7e-19)
     x
     (if (<= y 1.05e+181)
       (* z (* x (- a)))
       (if (<= y 4.6e+230) (* x (* y (- t))) (* a (* x (- z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.5e+19) {
		tmp = t * (x * -y);
	} else if (y <= 2.7e-19) {
		tmp = x;
	} else if (y <= 1.05e+181) {
		tmp = z * (x * -a);
	} else if (y <= 4.6e+230) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.5d+19)) then
        tmp = t * (x * -y)
    else if (y <= 2.7d-19) then
        tmp = x
    else if (y <= 1.05d+181) then
        tmp = z * (x * -a)
    else if (y <= 4.6d+230) then
        tmp = x * (y * -t)
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.5e+19) {
		tmp = t * (x * -y);
	} else if (y <= 2.7e-19) {
		tmp = x;
	} else if (y <= 1.05e+181) {
		tmp = z * (x * -a);
	} else if (y <= 4.6e+230) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.5e+19:
		tmp = t * (x * -y)
	elif y <= 2.7e-19:
		tmp = x
	elif y <= 1.05e+181:
		tmp = z * (x * -a)
	elif y <= 4.6e+230:
		tmp = x * (y * -t)
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.5e+19)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 2.7e-19)
		tmp = x;
	elseif (y <= 1.05e+181)
		tmp = Float64(z * Float64(x * Float64(-a)));
	elseif (y <= 4.6e+230)
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.5e+19)
		tmp = t * (x * -y);
	elseif (y <= 2.7e-19)
		tmp = x;
	elseif (y <= 1.05e+181)
		tmp = z * (x * -a);
	elseif (y <= 4.6e+230)
		tmp = x * (y * -t);
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.5e+19], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-19], x, If[LessEqual[y, 1.05e+181], N[(z * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+230], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.5e19

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 92.1%

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

   5. Taylor expanded in t around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. distribute-lft-neg-out 62.6%

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

      3. *-commutative 62.6%

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

   7. Simplified 62.6%

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

   8. Taylor expanded in y around 0 27.7%

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

      1. mul-1-neg 27.7%

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

      2. unsub-neg 27.7%

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

      3. *-commutative 27.7%

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

      4. associate-*l* 24.9%

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

      5. *-commutative 24.9%

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

   10. Simplified 24.9%

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

   11. Taylor expanded in t around inf 27.6%

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

   if -5.5e19 < y < 2.7000000000000001e-19

   1. Initial program 95.0%

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

   2. Taylor expanded in y around 0 83.3%

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

   3. Taylor expanded in a around 0 35.6%

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

   if 2.7000000000000001e-19 < y < 1.04999999999999999e181

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 40.5%

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

   3. Taylor expanded in b around 0 6.1%

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

   4. Taylor expanded in z around 0 6.2%

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

      1. mul-1-neg 6.2%

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

      2. unsub-neg 6.2%

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

   6. Simplified 6.2%

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

   7. Taylor expanded in a around inf 30.9%

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

      1. mul-1-neg 30.9%

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

      2. associate-*r* 33.0%

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

   9. Simplified 33.0%

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

   if 1.04999999999999999e181 < y < 4.5999999999999996e230

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 100.0%

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

   5. Taylor expanded in t around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. distribute-lft-neg-out 74.3%

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

      3. *-commutative 74.3%

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

   7. Simplified 74.3%

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

   8. Taylor expanded in y around 0 35.5%

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

      1. mul-1-neg 35.5%

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

      2. unsub-neg 35.5%

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

      3. *-commutative 35.5%

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

      4. associate-*l* 42.0%

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

      5. *-commutative 42.0%

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

   10. Simplified 42.0%

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

   11. Taylor expanded in t around inf 41.6%

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

       1. mul-1-neg 41.6%

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

       2. associate-*r* 41.6%

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

       3. *-commutative 41.6%

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

       4. distribute-rgt-neg-in 41.6%

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

       5. associate-*r* 48.0%

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

   13. Simplified 48.0%

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

   if 4.5999999999999996e230 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 27.3%

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

   3. Taylor expanded in b around 0 3.8%

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

   4. Taylor expanded in z around 0 3.8%

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

      1. mul-1-neg 3.8%

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

      2. unsub-neg 3.8%

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

   6. Simplified 3.8%

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

   7. Taylor expanded in a around inf 32.3%

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

      1. mul-1-neg 32.3%

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

      2. *-commutative 32.3%

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

      3. distribute-rgt-neg-in 32.3%

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

   9. Simplified 32.3%

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

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+181}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 11: 30.3% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(1 - z \cdot a\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.4e-21)
   (* t (* x (- y)))
   (if (<= y 2.7e-13)
     (* x (- 1.0 (* z a)))
     (if (<= y 3e+182)
       (* z (* x (- a)))
       (if (<= y 1.75e+230) (* x (* y (- t))) (* a (* x (- z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.4e-21) {
		tmp = t * (x * -y);
	} else if (y <= 2.7e-13) {
		tmp = x * (1.0 - (z * a));
	} else if (y <= 3e+182) {
		tmp = z * (x * -a);
	} else if (y <= 1.75e+230) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.4d-21)) then
        tmp = t * (x * -y)
    else if (y <= 2.7d-13) then
        tmp = x * (1.0d0 - (z * a))
    else if (y <= 3d+182) then
        tmp = z * (x * -a)
    else if (y <= 1.75d+230) then
        tmp = x * (y * -t)
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.4e-21) {
		tmp = t * (x * -y);
	} else if (y <= 2.7e-13) {
		tmp = x * (1.0 - (z * a));
	} else if (y <= 3e+182) {
		tmp = z * (x * -a);
	} else if (y <= 1.75e+230) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.4e-21:
		tmp = t * (x * -y)
	elif y <= 2.7e-13:
		tmp = x * (1.0 - (z * a))
	elif y <= 3e+182:
		tmp = z * (x * -a)
	elif y <= 1.75e+230:
		tmp = x * (y * -t)
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.4e-21)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 2.7e-13)
		tmp = Float64(x * Float64(1.0 - Float64(z * a)));
	elseif (y <= 3e+182)
		tmp = Float64(z * Float64(x * Float64(-a)));
	elseif (y <= 1.75e+230)
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.4e-21)
		tmp = t * (x * -y);
	elseif (y <= 2.7e-13)
		tmp = x * (1.0 - (z * a));
	elseif (y <= 3e+182)
		tmp = z * (x * -a);
	elseif (y <= 1.75e+230)
		tmp = x * (y * -t);
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.4e-21], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-13], N[(x * N[(1.0 - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+182], N[(z * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+230], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.3999999999999999e-21

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 88.8%

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

   5. Taylor expanded in t around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. distribute-lft-neg-out 62.7%

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

      3. *-commutative 62.7%

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

   7. Simplified 62.7%

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

   8. Taylor expanded in y around 0 24.9%

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

      1. mul-1-neg 24.9%

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

      2. unsub-neg 24.9%

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

      3. *-commutative 24.9%

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

      4. associate-*l* 22.4%

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

      5. *-commutative 22.4%

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

   10. Simplified 22.4%

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

   11. Taylor expanded in t around inf 24.8%

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

   if -2.3999999999999999e-21 < y < 2.70000000000000011e-13

   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 y around 0 84.7%

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

   3. Taylor expanded in b around 0 41.5%

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

   4. Taylor expanded in z around 0 40.3%

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

      1. mul-1-neg 40.3%

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

      2. unsub-neg 40.3%

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

   6. Simplified 40.3%

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

   if 2.70000000000000011e-13 < y < 3.0000000000000002e182

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 40.5%

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

   3. Taylor expanded in b around 0 6.1%

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

   4. Taylor expanded in z around 0 6.2%

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

      1. mul-1-neg 6.2%

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

      2. unsub-neg 6.2%

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

   6. Simplified 6.2%

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

   7. Taylor expanded in a around inf 30.9%

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

      1. mul-1-neg 30.9%

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

      2. associate-*r* 33.0%

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

   9. Simplified 33.0%

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

   if 3.0000000000000002e182 < y < 1.75e230

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 100.0%

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

   5. Taylor expanded in t around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. distribute-lft-neg-out 74.3%

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

      3. *-commutative 74.3%

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

   7. Simplified 74.3%

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

   8. Taylor expanded in y around 0 35.5%

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

      1. mul-1-neg 35.5%

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

      2. unsub-neg 35.5%

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

      3. *-commutative 35.5%

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

      4. associate-*l* 42.0%

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

      5. *-commutative 42.0%

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

   10. Simplified 42.0%

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

   11. Taylor expanded in t around inf 41.6%

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

       1. mul-1-neg 41.6%

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

       2. associate-*r* 41.6%

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

       3. *-commutative 41.6%

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

       4. distribute-rgt-neg-in 41.6%

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

       5. associate-*r* 48.0%

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

   13. Simplified 48.0%

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

   if 1.75e230 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 27.3%

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

   3. Taylor expanded in b around 0 3.8%

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

   4. Taylor expanded in z around 0 3.8%

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

      1. mul-1-neg 3.8%

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

      2. unsub-neg 3.8%

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

   6. Simplified 3.8%

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

   7. Taylor expanded in a around inf 32.3%

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

      1. mul-1-neg 32.3%

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

      2. *-commutative 32.3%

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

      3. distribute-rgt-neg-in 32.3%

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

   9. Simplified 32.3%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(1 - z \cdot a\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 12: 33.0% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.1e+68)
   (* t (* x (- y)))
   (if (<= y 6.8e-12)
     (- x (* b (* x a)))
     (if (<= y 5e+182)
       (* z (* x (- a)))
       (if (<= y 2.5e+230) (* x (* y (- t))) (* a (* x (- z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.1e+68) {
		tmp = t * (x * -y);
	} else if (y <= 6.8e-12) {
		tmp = x - (b * (x * a));
	} else if (y <= 5e+182) {
		tmp = z * (x * -a);
	} else if (y <= 2.5e+230) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.1d+68)) then
        tmp = t * (x * -y)
    else if (y <= 6.8d-12) then
        tmp = x - (b * (x * a))
    else if (y <= 5d+182) then
        tmp = z * (x * -a)
    else if (y <= 2.5d+230) then
        tmp = x * (y * -t)
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.1e+68) {
		tmp = t * (x * -y);
	} else if (y <= 6.8e-12) {
		tmp = x - (b * (x * a));
	} else if (y <= 5e+182) {
		tmp = z * (x * -a);
	} else if (y <= 2.5e+230) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.1e+68:
		tmp = t * (x * -y)
	elif y <= 6.8e-12:
		tmp = x - (b * (x * a))
	elif y <= 5e+182:
		tmp = z * (x * -a)
	elif y <= 2.5e+230:
		tmp = x * (y * -t)
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.1e+68)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 6.8e-12)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	elseif (y <= 5e+182)
		tmp = Float64(z * Float64(x * Float64(-a)));
	elseif (y <= 2.5e+230)
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.1e+68)
		tmp = t * (x * -y);
	elseif (y <= 6.8e-12)
		tmp = x - (b * (x * a));
	elseif (y <= 5e+182)
		tmp = z * (x * -a);
	elseif (y <= 2.5e+230)
		tmp = x * (y * -t);
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.1e+68], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-12], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+182], N[(z * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+230], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.0999999999999998e68

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 90.7%

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

   5. Taylor expanded in t around inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. distribute-lft-neg-out 61.6%

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

      3. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in y around 0 30.0%

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

      1. mul-1-neg 30.0%

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

      2. unsub-neg 30.0%

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

      3. *-commutative 30.0%

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

      4. associate-*l* 24.9%

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

      5. *-commutative 24.9%

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

   10. Simplified 24.9%

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

   11. Taylor expanded in t around inf 29.9%

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

   if -3.0999999999999998e68 < y < 6.8000000000000001e-12

   1. Initial program 95.3%

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

      1. fma-def 95.3%

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

      2. sub-neg 95.3%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

      1. add-log-exp 100.0%

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

      2. add-cube-cbrt 99.9%

         \[\leadsto x \cdot e^{\log \color{blue}{\left(\left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}} \cdot \sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}}\right) \cdot \sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}}\right)}} \]

      3. log-prod 99.9%

         \[\leadsto x \cdot e^{\color{blue}{\log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}} \cdot \sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}}\right) + \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}}\right)}} \]

   5. Applied egg-rr 91.3%

      \[\leadsto x \cdot e^{\color{blue}{\log \left({\left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)}^{2}\right) + \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)}} \]
   6. Step-by-step derivation

      1. log-pow 91.3%

         \[\leadsto x \cdot e^{\color{blue}{2 \cdot \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)} + \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)} \]

      2. distribute-lft1-in 91.3%

         \[\leadsto x \cdot e^{\color{blue}{\left(2 + 1\right) \cdot \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)}} \]

      3. metadata-eval 91.3%

         \[\leadsto x \cdot e^{\color{blue}{3} \cdot \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)} \]

   7. Simplified 91.3%

      \[\leadsto x \cdot e^{\color{blue}{3 \cdot \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)}} \]

   8. Taylor expanded in b around inf 77.6%

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

      1. mul-1-neg 77.6%

         \[\leadsto x \cdot e^{3 \cdot \log \left(\sqrt[3]{e^{\color{blue}{-a \cdot b}}}\right)} \]

      2. *-commutative 77.6%

         \[\leadsto x \cdot e^{3 \cdot \log \left(\sqrt[3]{e^{-\color{blue}{b \cdot a}}}\right)} \]

      3. distribute-rgt-neg-in 77.6%

         \[\leadsto x \cdot e^{3 \cdot \log \left(\sqrt[3]{e^{\color{blue}{b \cdot \left(-a\right)}}}\right)} \]

   10. Simplified 77.6%

       \[\leadsto x \cdot e^{3 \cdot \log \left(\sqrt[3]{e^{\color{blue}{b \cdot \left(-a\right)}}}\right)} \]

   11. Taylor expanded in b around 0 44.3%

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

       1. mul-1-neg 44.3%

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

       2. unsub-neg 44.3%

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

       3. associate-*r* 46.6%

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

       4. *-commutative 46.6%

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

       5. associate-*l* 45.6%

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

   13. Simplified 45.6%

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

   if 6.8000000000000001e-12 < y < 4.99999999999999973e182

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 40.5%

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

   3. Taylor expanded in b around 0 6.1%

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

   4. Taylor expanded in z around 0 6.2%

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

      1. mul-1-neg 6.2%

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

      2. unsub-neg 6.2%

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

   6. Simplified 6.2%

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

   7. Taylor expanded in a around inf 30.9%

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

      1. mul-1-neg 30.9%

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

      2. associate-*r* 33.0%

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

   9. Simplified 33.0%

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

   if 4.99999999999999973e182 < y < 2.5000000000000001e230

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 100.0%

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

   5. Taylor expanded in t around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. distribute-lft-neg-out 74.3%

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

      3. *-commutative 74.3%

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

   7. Simplified 74.3%

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

   8. Taylor expanded in y around 0 35.5%

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

      1. mul-1-neg 35.5%

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

      2. unsub-neg 35.5%

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

      3. *-commutative 35.5%

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

      4. associate-*l* 42.0%

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

      5. *-commutative 42.0%

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

   10. Simplified 42.0%

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

   11. Taylor expanded in t around inf 41.6%

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

       1. mul-1-neg 41.6%

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

       2. associate-*r* 41.6%

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

       3. *-commutative 41.6%

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

       4. distribute-rgt-neg-in 41.6%

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

       5. associate-*r* 48.0%

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

   13. Simplified 48.0%

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

   if 2.5000000000000001e230 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 27.3%

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

   3. Taylor expanded in b around 0 3.8%

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

   4. Taylor expanded in z around 0 3.8%

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

      1. mul-1-neg 3.8%

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

      2. unsub-neg 3.8%

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

   6. Simplified 3.8%

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

   7. Taylor expanded in a around inf 32.3%

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

      1. mul-1-neg 32.3%

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

      2. *-commutative 32.3%

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

      3. distribute-rgt-neg-in 32.3%

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

   9. Simplified 32.3%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 13: 33.0% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+72}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-15}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+179}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+229}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.6e+72)
   (- x (* t (* x y)))
   (if (<= y 6e-15)
     (- x (* b (* x a)))
     (if (<= y 6.5e+179)
       (* z (* x (- a)))
       (if (<= y 8.5e+229) (* x (* y (- t))) (* a (* x (- z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.6e+72) {
		tmp = x - (t * (x * y));
	} else if (y <= 6e-15) {
		tmp = x - (b * (x * a));
	} else if (y <= 6.5e+179) {
		tmp = z * (x * -a);
	} else if (y <= 8.5e+229) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.6d+72)) then
        tmp = x - (t * (x * y))
    else if (y <= 6d-15) then
        tmp = x - (b * (x * a))
    else if (y <= 6.5d+179) then
        tmp = z * (x * -a)
    else if (y <= 8.5d+229) then
        tmp = x * (y * -t)
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.6e+72) {
		tmp = x - (t * (x * y));
	} else if (y <= 6e-15) {
		tmp = x - (b * (x * a));
	} else if (y <= 6.5e+179) {
		tmp = z * (x * -a);
	} else if (y <= 8.5e+229) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.6e+72:
		tmp = x - (t * (x * y))
	elif y <= 6e-15:
		tmp = x - (b * (x * a))
	elif y <= 6.5e+179:
		tmp = z * (x * -a)
	elif y <= 8.5e+229:
		tmp = x * (y * -t)
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.6e+72)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (y <= 6e-15)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	elseif (y <= 6.5e+179)
		tmp = Float64(z * Float64(x * Float64(-a)));
	elseif (y <= 8.5e+229)
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.6e+72)
		tmp = x - (t * (x * y));
	elseif (y <= 6e-15)
		tmp = x - (b * (x * a));
	elseif (y <= 6.5e+179)
		tmp = z * (x * -a);
	elseif (y <= 8.5e+229)
		tmp = x * (y * -t);
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.6e+72], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-15], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+179], N[(z * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+229], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.6e72

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 90.7%

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

   5. Taylor expanded in t around inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. distribute-lft-neg-out 61.6%

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

      3. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in y around 0 30.0%

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

      1. mul-1-neg 30.0%

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

      2. unsub-neg 30.0%

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

      3. *-commutative 30.0%

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

      4. associate-*l* 24.9%

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

      5. *-commutative 24.9%

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

   10. Simplified 24.9%

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

   11. Taylor expanded in x around 0 30.0%

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

   if -6.6e72 < y < 6e-15

   1. Initial program 95.3%

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

      1. fma-def 95.3%

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

      2. sub-neg 95.3%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

      1. add-log-exp 100.0%

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

      2. add-cube-cbrt 99.9%

         \[\leadsto x \cdot e^{\log \color{blue}{\left(\left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}} \cdot \sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}}\right) \cdot \sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}}\right)}} \]

      3. log-prod 99.9%

         \[\leadsto x \cdot e^{\color{blue}{\log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}} \cdot \sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}}\right) + \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}}\right)}} \]

   5. Applied egg-rr 91.3%

      \[\leadsto x \cdot e^{\color{blue}{\log \left({\left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)}^{2}\right) + \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)}} \]
   6. Step-by-step derivation

      1. log-pow 91.3%

         \[\leadsto x \cdot e^{\color{blue}{2 \cdot \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)} + \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)} \]

      2. distribute-lft1-in 91.3%

         \[\leadsto x \cdot e^{\color{blue}{\left(2 + 1\right) \cdot \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)}} \]

      3. metadata-eval 91.3%

         \[\leadsto x \cdot e^{\color{blue}{3} \cdot \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)} \]

   7. Simplified 91.3%

      \[\leadsto x \cdot e^{\color{blue}{3 \cdot \log \left(\sqrt[3]{e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(z\right) - b\right)\right)}}\right)}} \]

   8. Taylor expanded in b around inf 77.6%

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

      1. mul-1-neg 77.6%

         \[\leadsto x \cdot e^{3 \cdot \log \left(\sqrt[3]{e^{\color{blue}{-a \cdot b}}}\right)} \]

      2. *-commutative 77.6%

         \[\leadsto x \cdot e^{3 \cdot \log \left(\sqrt[3]{e^{-\color{blue}{b \cdot a}}}\right)} \]

      3. distribute-rgt-neg-in 77.6%

         \[\leadsto x \cdot e^{3 \cdot \log \left(\sqrt[3]{e^{\color{blue}{b \cdot \left(-a\right)}}}\right)} \]

   10. Simplified 77.6%

       \[\leadsto x \cdot e^{3 \cdot \log \left(\sqrt[3]{e^{\color{blue}{b \cdot \left(-a\right)}}}\right)} \]

   11. Taylor expanded in b around 0 44.3%

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

       1. mul-1-neg 44.3%

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

       2. unsub-neg 44.3%

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

       3. associate-*r* 46.6%

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

       4. *-commutative 46.6%

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

       5. associate-*l* 45.6%

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

   13. Simplified 45.6%

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

   if 6e-15 < y < 6.50000000000000052e179

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 40.5%

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

   3. Taylor expanded in b around 0 6.1%

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

   4. Taylor expanded in z around 0 6.2%

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

      1. mul-1-neg 6.2%

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

      2. unsub-neg 6.2%

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

   6. Simplified 6.2%

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

   7. Taylor expanded in a around inf 30.9%

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

      1. mul-1-neg 30.9%

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

      2. associate-*r* 33.0%

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

   9. Simplified 33.0%

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

   if 6.50000000000000052e179 < y < 8.49999999999999966e229

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 100.0%

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

   5. Taylor expanded in t around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. distribute-lft-neg-out 74.3%

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

      3. *-commutative 74.3%

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

   7. Simplified 74.3%

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

   8. Taylor expanded in y around 0 35.5%

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

      1. mul-1-neg 35.5%

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

      2. unsub-neg 35.5%

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

      3. *-commutative 35.5%

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

      4. associate-*l* 42.0%

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

      5. *-commutative 42.0%

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

   10. Simplified 42.0%

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

   11. Taylor expanded in t around inf 41.6%

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

       1. mul-1-neg 41.6%

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

       2. associate-*r* 41.6%

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

       3. *-commutative 41.6%

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

       4. distribute-rgt-neg-in 41.6%

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

       5. associate-*r* 48.0%

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

   13. Simplified 48.0%

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

   if 8.49999999999999966e229 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 27.3%

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

   3. Taylor expanded in b around 0 3.8%

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

   4. Taylor expanded in z around 0 3.8%

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

      1. mul-1-neg 3.8%

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

      2. unsub-neg 3.8%

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

   6. Simplified 3.8%

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

   7. Taylor expanded in a around inf 32.3%

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

      1. mul-1-neg 32.3%

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

      2. *-commutative 32.3%

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

      3. distribute-rgt-neg-in 32.3%

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

   9. Simplified 32.3%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+72}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-15}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+179}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+229}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 14: 34.2% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+70}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-11}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+229}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.6e+70)
   (- x (* t (* x y)))
   (if (<= y 3.5e-11)
     (- x (* x (* a b)))
     (if (<= y 4e+186)
       (* z (* x (- a)))
       (if (<= y 9.5e+229) (* x (* y (- t))) (* a (* x (- z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.6e+70) {
		tmp = x - (t * (x * y));
	} else if (y <= 3.5e-11) {
		tmp = x - (x * (a * b));
	} else if (y <= 4e+186) {
		tmp = z * (x * -a);
	} else if (y <= 9.5e+229) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.6d+70)) then
        tmp = x - (t * (x * y))
    else if (y <= 3.5d-11) then
        tmp = x - (x * (a * b))
    else if (y <= 4d+186) then
        tmp = z * (x * -a)
    else if (y <= 9.5d+229) then
        tmp = x * (y * -t)
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.6e+70) {
		tmp = x - (t * (x * y));
	} else if (y <= 3.5e-11) {
		tmp = x - (x * (a * b));
	} else if (y <= 4e+186) {
		tmp = z * (x * -a);
	} else if (y <= 9.5e+229) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.6e+70:
		tmp = x - (t * (x * y))
	elif y <= 3.5e-11:
		tmp = x - (x * (a * b))
	elif y <= 4e+186:
		tmp = z * (x * -a)
	elif y <= 9.5e+229:
		tmp = x * (y * -t)
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.6e+70)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (y <= 3.5e-11)
		tmp = Float64(x - Float64(x * Float64(a * b)));
	elseif (y <= 4e+186)
		tmp = Float64(z * Float64(x * Float64(-a)));
	elseif (y <= 9.5e+229)
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.6e+70)
		tmp = x - (t * (x * y));
	elseif (y <= 3.5e-11)
		tmp = x - (x * (a * b));
	elseif (y <= 4e+186)
		tmp = z * (x * -a);
	elseif (y <= 9.5e+229)
		tmp = x * (y * -t);
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.6e+70], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-11], N[(x - N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+186], N[(z * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+229], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.6e70

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 90.7%

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

   5. Taylor expanded in t around inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. distribute-lft-neg-out 61.6%

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

      3. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in y around 0 30.0%

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

      1. mul-1-neg 30.0%

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

      2. unsub-neg 30.0%

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

      3. *-commutative 30.0%

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

      4. associate-*l* 24.9%

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

      5. *-commutative 24.9%

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

   10. Simplified 24.9%

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

   11. Taylor expanded in x around 0 30.0%

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

   if -2.6e70 < y < 3.50000000000000019e-11

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0 80.7%

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

   3. Taylor expanded in z around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. *-commutative 77.6%

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

      3. distribute-rgt-neg-in 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in b around 0 44.3%

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

      1. mul-1-neg 44.3%

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

      2. unsub-neg 44.3%

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

      3. associate-*r* 46.6%

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

      4. *-commutative 46.6%

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

   8. Simplified 46.6%

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

   if 3.50000000000000019e-11 < y < 3.99999999999999992e186

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 40.5%

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

   3. Taylor expanded in b around 0 6.1%

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

   4. Taylor expanded in z around 0 6.2%

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

      1. mul-1-neg 6.2%

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

      2. unsub-neg 6.2%

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

   6. Simplified 6.2%

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

   7. Taylor expanded in a around inf 30.9%

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

      1. mul-1-neg 30.9%

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

      2. associate-*r* 33.0%

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

   9. Simplified 33.0%

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

   if 3.99999999999999992e186 < y < 9.5e229

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 100.0%

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

   5. Taylor expanded in t around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. distribute-lft-neg-out 74.3%

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

      3. *-commutative 74.3%

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

   7. Simplified 74.3%

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

   8. Taylor expanded in y around 0 35.5%

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

      1. mul-1-neg 35.5%

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

      2. unsub-neg 35.5%

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

      3. *-commutative 35.5%

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

      4. associate-*l* 42.0%

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

      5. *-commutative 42.0%

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

   10. Simplified 42.0%

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

   11. Taylor expanded in t around inf 41.6%

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

       1. mul-1-neg 41.6%

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

       2. associate-*r* 41.6%

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

       3. *-commutative 41.6%

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

       4. distribute-rgt-neg-in 41.6%

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

       5. associate-*r* 48.0%

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

   13. Simplified 48.0%

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

   if 9.5e229 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 27.3%

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

   3. Taylor expanded in b around 0 3.8%

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

   4. Taylor expanded in z around 0 3.8%

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

      1. mul-1-neg 3.8%

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

      2. unsub-neg 3.8%

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

   6. Simplified 3.8%

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

   7. Taylor expanded in a around inf 32.3%

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

      1. mul-1-neg 32.3%

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

      2. *-commutative 32.3%

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

      3. distribute-rgt-neg-in 32.3%

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

   9. Simplified 32.3%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+70}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-11}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+229}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 15: 28.0% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-11} \lor \neg \left(y \leq 1.8 \cdot 10^{-11}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.8e-11) (not (<= y 1.8e-11))) (* z (* x (- a))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.8e-11) || !(y <= 1.8e-11)) {
		tmp = z * (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 <= (-2.8d-11)) .or. (.not. (y <= 1.8d-11))) then
        tmp = z * (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 <= -2.8e-11) || !(y <= 1.8e-11)) {
		tmp = z * (x * -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.8e-11) or not (y <= 1.8e-11):
		tmp = z * (x * -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.8e-11) || !(y <= 1.8e-11))
		tmp = Float64(z * 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 <= -2.8e-11) || ~((y <= 1.8e-11)))
		tmp = z * (x * -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.8e-11], N[Not[LessEqual[y, 1.8e-11]], $MachinePrecision]], N[(z * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e-11 or 1.79999999999999992e-11 < y

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 37.0%

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

   3. Taylor expanded in b around 0 4.7%

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

   4. Taylor expanded in z around 0 4.6%

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

      1. mul-1-neg 4.6%

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

      2. unsub-neg 4.6%

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

   6. Simplified 4.6%

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

   7. Taylor expanded in a around inf 21.9%

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

      1. mul-1-neg 21.9%

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

      2. associate-*r* 23.5%

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

   9. Simplified 23.5%

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

   if -2.8e-11 < y < 1.79999999999999992e-11

   1. Initial program 94.8%

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

   2. Taylor expanded in y around 0 84.3%

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

   3. Taylor expanded in a around 0 37.0%

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

4. Final simplification 29.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-11} \lor \neg \left(y \leq 1.8 \cdot 10^{-11}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 20.0% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

2. Taylor expanded in y around 0 57.7%

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

3. Taylor expanded in a around 0 18.5%

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

4. Final simplification 18.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023320 
(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))))))