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

Percentage Accurate: 96.7% → 99.3%

Time: 17.3s

Alternatives: 14

Speedup: 1.5×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% 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 96.9%

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

2. Taylor expanded in z around 0 100.0%

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

   1. associate-*r* 100.0%

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

   2. associate-*r* 100.0%

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

   3. distribute-lft-out 100.0%

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

   4. neg-mul-1 100.0%

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

4. Simplified 100.0%

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

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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-114} \lor \neg \left(a \leq 1.7 \cdot 10^{-151}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right) - y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -9.2e-114) (not (<= a 1.7e-151)))
   (* x (exp (- (* a (- b)) (* y t))))
   (* x (exp (* y (- (log z) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -9.2e-114) || !(a <= 1.7e-151)) {
		tmp = x * exp(((a * -b) - (y * t)));
	} else {
		tmp = x * exp((y * (log(z) - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-9.2d-114)) .or. (.not. (a <= 1.7d-151))) then
        tmp = x * exp(((a * -b) - (y * t)))
    else
        tmp = x * exp((y * (log(z) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -9.2e-114) || !(a <= 1.7e-151)) {
		tmp = x * Math.exp(((a * -b) - (y * t)));
	} else {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -9.2e-114) or not (a <= 1.7e-151):
		tmp = x * math.exp(((a * -b) - (y * t)))
	else:
		tmp = x * math.exp((y * (math.log(z) - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -9.2e-114) || !(a <= 1.7e-151))
		tmp = Float64(x * exp(Float64(Float64(a * Float64(-b)) - Float64(y * t))));
	else
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -9.2e-114) || ~((a <= 1.7e-151)))
		tmp = x * exp(((a * -b) - (y * t)));
	else
		tmp = x * exp((y * (log(z) - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -9.2e-114], N[Not[LessEqual[a, 1.7e-151]], $MachinePrecision]], N[(x * N[Exp[N[(N[(a * (-b)), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.1999999999999997e-114 or 1.7000000000000001e-151 < a

   1. Initial program 95.7%

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

   2. Taylor expanded in z around 0 94.6%

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

      1. fma-def 94.6%

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

      2. mul-1-neg 94.6%

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

      3. fma-neg 94.6%

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

      4. *-commutative 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in t around inf 89.4%

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

      1. neg-mul-1 50.9%

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

   7. Simplified 89.4%

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

   if -9.1999999999999997e-114 < a < 1.7000000000000001e-151

   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 a around 0 94.6%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-114} \lor \neg \left(a \leq 1.7 \cdot 10^{-151}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right) - y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \end{array} \]

Alternative 3: 96.1% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in z around 0 96.1%

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

   1. fma-def 96.1%

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

   2. mul-1-neg 96.1%

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

   3. fma-neg 96.1%

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

   4. *-commutative 96.1%

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

4. Simplified 96.1%

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

5. Final simplification 96.1%

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

Alternative 4: 54.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+185} \lor \neg \left(a \leq 4.6 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot e^{z \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -5.4e+185) (not (<= a 4.6e+61)))
   (* x (exp (* z (- a))))
   (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -5.4e+185) || !(a <= 4.6e+61)) {
		tmp = x * exp((z * -a));
	} 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 ((a <= (-5.4d+185)) .or. (.not. (a <= 4.6d+61))) then
        tmp = x * exp((z * -a))
    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 ((a <= -5.4e+185) || !(a <= 4.6e+61)) {
		tmp = x * Math.exp((z * -a));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -5.4e+185) or not (a <= 4.6e+61):
		tmp = x * math.exp((z * -a))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -5.4e+185) || !(a <= 4.6e+61))
		tmp = Float64(x * exp(Float64(z * Float64(-a))));
	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 ((a <= -5.4e+185) || ~((a <= 4.6e+61)))
		tmp = x * exp((z * -a));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -5.4e+185], N[Not[LessEqual[a, 4.6e+61]], $MachinePrecision]], N[(x * N[Exp[N[(z * (-a)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.40000000000000013e185 or 4.5999999999999999e61 < a

   1. Initial program 89.6%

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

   2. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. neg-mul-1 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 44.5%

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

      1. mul-1-neg 44.5%

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

      2. distribute-lft-neg-out 44.5%

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

      3. *-commutative 44.5%

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

   7. Simplified 44.5%

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

   if -5.40000000000000013e185 < a < 4.5999999999999999e61

   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 a around 0 82.2%

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

   3. Taylor expanded in t around 0 61.3%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+185} \lor \neg \left(a \leq 4.6 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot e^{z \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 5: 70.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.98 \cdot 10^{+29} \lor \neg \left(t \leq 2 \cdot 10^{-84}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.98e+29) (not (<= t 2e-84)))
   (* x (exp (* 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 <= -2.98e+29) || !(t <= 2e-84)) {
		tmp = x * exp((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 <= (-2.98d+29)) .or. (.not. (t <= 2d-84))) then
        tmp = x * exp((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 <= -2.98e+29) || !(t <= 2e-84)) {
		tmp = x * Math.exp((y * -t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.98e+29) or not (t <= 2e-84):
		tmp = x * math.exp((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 <= -2.98e+29) || !(t <= 2e-84))
		tmp = Float64(x * exp(Float64(y * Float64(-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 <= -2.98e+29) || ~((t <= 2e-84)))
		tmp = x * exp((y * -t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.98e+29], N[Not[LessEqual[t, 2e-84]], $MachinePrecision]], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9799999999999999e29 or 2.0000000000000001e-84 < t

   1. Initial program 98.5%

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

   2. Taylor expanded in a around 0 75.0%

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

   3. Taylor expanded in t around inf 75.0%

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

      1. neg-mul-1 75.0%

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

   5. Simplified 75.0%

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

   if -2.9799999999999999e29 < t < 2.0000000000000001e-84

   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 a around 0 63.2%

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

   3. Taylor expanded in t around 0 63.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.98 \cdot 10^{+29} \lor \neg \left(t \leq 2 \cdot 10^{-84}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 6: 69.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-94} \lor \neg \left(b \leq 1.32 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.5e-94) (not (<= b 1.32e-8)))
   (* 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 ((b <= -9.5e-94) || !(b <= 1.32e-8)) {
		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 ((b <= (-9.5d-94)) .or. (.not. (b <= 1.32d-8))) 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 ((b <= -9.5e-94) || !(b <= 1.32e-8)) {
		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 (b <= -9.5e-94) or not (b <= 1.32e-8):
		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 ((b <= -9.5e-94) || !(b <= 1.32e-8))
		tmp = Float64(x * exp(Float64(a * Float64(-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 ((b <= -9.5e-94) || ~((b <= 1.32e-8)))
		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[Or[LessEqual[b, -9.5e-94], N[Not[LessEqual[b, 1.32e-8]], $MachinePrecision]], 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 2 regimes

2. if b < -9.4999999999999997e-94 or 1.32000000000000007e-8 < b

   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 z around 0 98.6%

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

      1. fma-def 98.6%

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

      2. mul-1-neg 98.6%

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

      3. fma-neg 98.6%

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

      4. *-commutative 98.6%

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

   4. Simplified 98.6%

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

   5. Taylor expanded in y around 0 74.5%

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

   if -9.4999999999999997e-94 < b < 1.32000000000000007e-8

   1. Initial program 93.9%

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

   2. Taylor expanded in a around 0 87.3%

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

   3. Taylor expanded in t around inf 70.0%

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

      1. neg-mul-1 70.0%

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

   5. Simplified 70.0%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-94} \lor \neg \left(b \leq 1.32 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 7: 84.0% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in z around 0 96.1%

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

   1. fma-def 96.1%

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

   2. mul-1-neg 96.1%

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

   3. fma-neg 96.1%

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

   4. *-commutative 96.1%

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

4. Simplified 96.1%

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

5. Taylor expanded in t around inf 85.2%

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

   1. neg-mul-1 55.8%

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

7. Simplified 85.2%

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

8. Final simplification 85.2%

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

Alternative 8: 56.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0032 \lor \neg \left(y \leq 3.7 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.0032) (not (<= y 3.7e-16)))
   (* x (pow z y))
   (* x (- 1.0 (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.0032) || !(y <= 3.7e-16)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-0.0032d0)) .or. (.not. (y <= 3.7d-16))) then
        tmp = x * (z ** y)
    else
        tmp = x * (1.0d0 - (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.0032) || !(y <= 3.7e-16)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -0.0032) or not (y <= 3.7e-16):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * (1.0 - (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -0.0032) || !(y <= 3.7e-16))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -0.0032) || ~((y <= 3.7e-16)))
		tmp = x * (z ^ y);
	else
		tmp = x * (1.0 - (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -0.0032], N[Not[LessEqual[y, 3.7e-16]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00320000000000000015 or 3.7e-16 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in a around 0 82.2%

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

   3. Taylor expanded in t around 0 63.6%

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

   if -0.00320000000000000015 < y < 3.7e-16

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 93.9%

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

      1. fma-def 93.9%

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

      2. mul-1-neg 93.9%

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

      3. fma-neg 93.9%

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

      4. *-commutative 93.9%

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

   4. Simplified 93.9%

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

   5. Taylor expanded in y around 0 77.5%

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

   6. Taylor expanded in a around 0 45.9%

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

      1. mul-1-neg 45.9%

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

      2. *-commutative 45.9%

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

      3. unsub-neg 45.9%

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

      4. *-commutative 45.9%

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

   8. Simplified 45.9%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0032 \lor \neg \left(y \leq 3.7 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \]

Alternative 9: 28.1% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y \cdot t\right)\\ t_2 := b \cdot \left(-x \cdot a\right)\\ \mathbf{if}\;a \leq -3.05 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-230}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (* y t)))) (t_2 (* b (- (* x a)))))
   (if (<= a -3.05e+131)
     t_2
     (if (<= a -5.2e-256)
       t_1
       (if (<= a 3.5e-230) t_2 (if (<= a 1.02e+61) t_1 (* a (* x (- b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 - (y * t));
	double t_2 = b * -(x * a);
	double tmp;
	if (a <= -3.05e+131) {
		tmp = t_2;
	} else if (a <= -5.2e-256) {
		tmp = t_1;
	} else if (a <= 3.5e-230) {
		tmp = t_2;
	} else if (a <= 1.02e+61) {
		tmp = t_1;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y * t))
    t_2 = b * -(x * a)
    if (a <= (-3.05d+131)) then
        tmp = t_2
    else if (a <= (-5.2d-256)) then
        tmp = t_1
    else if (a <= 3.5d-230) then
        tmp = t_2
    else if (a <= 1.02d+61) then
        tmp = t_1
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 - (y * t));
	double t_2 = b * -(x * a);
	double tmp;
	if (a <= -3.05e+131) {
		tmp = t_2;
	} else if (a <= -5.2e-256) {
		tmp = t_1;
	} else if (a <= 3.5e-230) {
		tmp = t_2;
	} else if (a <= 1.02e+61) {
		tmp = t_1;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (1.0 - (y * t))
	t_2 = b * -(x * a)
	tmp = 0
	if a <= -3.05e+131:
		tmp = t_2
	elif a <= -5.2e-256:
		tmp = t_1
	elif a <= 3.5e-230:
		tmp = t_2
	elif a <= 1.02e+61:
		tmp = t_1
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(1.0 - Float64(y * t)))
	t_2 = Float64(b * Float64(-Float64(x * a)))
	tmp = 0.0
	if (a <= -3.05e+131)
		tmp = t_2;
	elseif (a <= -5.2e-256)
		tmp = t_1;
	elseif (a <= 3.5e-230)
		tmp = t_2;
	elseif (a <= 1.02e+61)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (1.0 - (y * t));
	t_2 = b * -(x * a);
	tmp = 0.0;
	if (a <= -3.05e+131)
		tmp = t_2;
	elseif (a <= -5.2e-256)
		tmp = t_1;
	elseif (a <= 3.5e-230)
		tmp = t_2;
	elseif (a <= 1.02e+61)
		tmp = t_1;
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * (-N[(x * a), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[a, -3.05e+131], t$95$2, If[LessEqual[a, -5.2e-256], t$95$1, If[LessEqual[a, 3.5e-230], t$95$2, If[LessEqual[a, 1.02e+61], t$95$1, N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.0499999999999999e131 or -5.2000000000000002e-256 < a < 3.49999999999999988e-230

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0 90.9%

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

      1. fma-def 90.9%

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

      2. mul-1-neg 90.9%

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

      3. fma-neg 90.9%

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

      4. *-commutative 90.9%

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

   4. Simplified 90.9%

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

   5. Taylor expanded in y around 0 56.9%

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

   6. Taylor expanded in a around 0 27.0%

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

      1. +-commutative 27.0%

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

      2. mul-1-neg 27.0%

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

      3. unsub-neg 27.0%

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

   8. Simplified 27.0%

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

   9. Taylor expanded in a around inf 35.6%

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

       1. mul-1-neg 35.6%

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

       2. associate-*r* 37.1%

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

       3. *-commutative 37.1%

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

       4. distribute-rgt-neg-out 37.1%

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

       5. associate-*l* 42.9%

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

   11. Simplified 42.9%

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

   if -3.0499999999999999e131 < a < -5.2000000000000002e-256 or 3.49999999999999988e-230 < a < 1.01999999999999999e61

   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 a around 0 82.1%

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

   3. Taylor expanded in t around inf 67.1%

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

      1. neg-mul-1 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in t around 0 37.6%

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

      1. +-commutative 37.6%

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

      2. mul-1-neg 37.6%

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

      3. unsub-neg 37.6%

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

      4. *-commutative 37.6%

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

   8. Simplified 37.6%

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

   if 1.01999999999999999e61 < a

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 93.3%

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

      1. fma-def 93.3%

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

      2. mul-1-neg 93.3%

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

      3. fma-neg 93.3%

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

      4. *-commutative 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in y around 0 71.4%

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

   6. Taylor expanded in a around 0 29.6%

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

      1. +-commutative 29.6%

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

      2. mul-1-neg 29.6%

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

      3. unsub-neg 29.6%

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

   8. Simplified 29.6%

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

   9. Taylor expanded in a around inf 33.8%

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

       1. mul-1-neg 33.8%

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

       2. distribute-rgt-neg-in 33.8%

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

       3. distribute-rgt-neg-in 33.8%

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

   11. Simplified 33.8%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.05 \cdot 10^{+131}:\\ \;\;\;\;b \cdot \left(-x \cdot a\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-230}:\\ \;\;\;\;b \cdot \left(-x \cdot a\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 10: 33.2% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;y \leq 520000000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.8e+84)
   (* x (- 1.0 (* y t)))
   (if (<= y 520000000000.0) (* x (- 1.0 (* a b))) (* b (- (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e+84) {
		tmp = x * (1.0 - (y * t));
	} else if (y <= 520000000000.0) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = b * -(x * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.8d+84)) then
        tmp = x * (1.0d0 - (y * t))
    else if (y <= 520000000000.0d0) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = b * -(x * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e+84) {
		tmp = x * (1.0 - (y * t));
	} else if (y <= 520000000000.0) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = b * -(x * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.8e+84:
		tmp = x * (1.0 - (y * t))
	elif y <= 520000000000.0:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = b * -(x * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.8e+84)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif (y <= 520000000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(b * Float64(-Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.8e+84)
		tmp = x * (1.0 - (y * t));
	elseif (y <= 520000000000.0)
		tmp = x * (1.0 - (a * b));
	else
		tmp = b * -(x * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.8e+84], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 520000000000.0], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * (-N[(x * a), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e84

   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 a around 0 85.2%

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

   3. Taylor expanded in t around inf 65.8%

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

      1. neg-mul-1 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in t around 0 29.2%

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

      1. +-commutative 29.2%

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

      2. mul-1-neg 29.2%

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

      3. unsub-neg 29.2%

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

      4. *-commutative 29.2%

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

   8. Simplified 29.2%

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

   if -1.8e84 < y < 5.2e11

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 94.1%

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

      1. fma-def 94.1%

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

      2. mul-1-neg 94.1%

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

      3. fma-neg 94.1%

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

      4. *-commutative 94.1%

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

   4. Simplified 94.1%

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

   5. Taylor expanded in y around 0 74.3%

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

   6. Taylor expanded in a around 0 42.9%

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

      1. mul-1-neg 42.9%

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

      2. *-commutative 42.9%

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

      3. unsub-neg 42.9%

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

      4. *-commutative 42.9%

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

   8. Simplified 42.9%

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

   if 5.2e11 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0 98.5%

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

      1. fma-def 98.5%

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

      2. mul-1-neg 98.5%

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

      3. fma-neg 98.5%

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

      4. *-commutative 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in y around 0 33.1%

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

   6. Taylor expanded in a around 0 10.8%

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

      1. +-commutative 10.8%

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

      2. mul-1-neg 10.8%

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

      3. unsub-neg 10.8%

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

   8. Simplified 10.8%

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

   9. Taylor expanded in a around inf 25.5%

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

       1. mul-1-neg 25.5%

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

       2. associate-*r* 28.4%

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

       3. *-commutative 28.4%

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

       4. distribute-rgt-neg-out 28.4%

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

       5. associate-*l* 31.3%

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

   11. Simplified 31.3%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;y \leq 520000000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-x \cdot a\right)\\ \end{array} \]

Alternative 11: 32.0% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;y \leq 0.021:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1e+82)
   (* x (- 1.0 (* y t)))
   (if (<= y 0.021) (- x (* a (* x b))) (* b (- (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1e+82) {
		tmp = x * (1.0 - (y * t));
	} else if (y <= 0.021) {
		tmp = x - (a * (x * b));
	} else {
		tmp = b * -(x * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1d+82)) then
        tmp = x * (1.0d0 - (y * t))
    else if (y <= 0.021d0) then
        tmp = x - (a * (x * b))
    else
        tmp = b * -(x * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1e+82) {
		tmp = x * (1.0 - (y * t));
	} else if (y <= 0.021) {
		tmp = x - (a * (x * b));
	} else {
		tmp = b * -(x * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1e+82:
		tmp = x * (1.0 - (y * t))
	elif y <= 0.021:
		tmp = x - (a * (x * b))
	else:
		tmp = b * -(x * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1e+82)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif (y <= 0.021)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	else
		tmp = Float64(b * Float64(-Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1e+82)
		tmp = x * (1.0 - (y * t));
	elseif (y <= 0.021)
		tmp = x - (a * (x * b));
	else
		tmp = b * -(x * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1e+82], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.021], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * (-N[(x * a), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.9999999999999996e81

   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 a around 0 85.2%

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

   3. Taylor expanded in t around inf 65.8%

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

      1. neg-mul-1 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in t around 0 29.2%

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

      1. +-commutative 29.2%

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

      2. mul-1-neg 29.2%

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

      3. unsub-neg 29.2%

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

      4. *-commutative 29.2%

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

   8. Simplified 29.2%

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

   if -9.9999999999999996e81 < y < 0.0210000000000000013

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 94.1%

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

      1. fma-def 94.1%

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

      2. mul-1-neg 94.1%

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

      3. fma-neg 94.1%

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

      4. *-commutative 94.1%

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

   4. Simplified 94.1%

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

   5. Taylor expanded in y around 0 74.2%

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

   6. Taylor expanded in a around 0 43.7%

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

      1. +-commutative 43.7%

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

      2. mul-1-neg 43.7%

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

      3. unsub-neg 43.7%

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

   8. Simplified 43.7%

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

   if 0.0210000000000000013 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0 98.5%

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

      1. fma-def 98.5%

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

      2. mul-1-neg 98.5%

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

      3. fma-neg 98.5%

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

      4. *-commutative 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in y around 0 34.1%

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

   6. Taylor expanded in a around 0 10.7%

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

      1. +-commutative 10.7%

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

      2. mul-1-neg 10.7%

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

      3. unsub-neg 10.7%

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

   8. Simplified 10.7%

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

   9. Taylor expanded in a around inf 25.2%

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

       1. mul-1-neg 25.2%

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

       2. associate-*r* 28.0%

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

       3. *-commutative 28.0%

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

       4. distribute-rgt-neg-out 28.0%

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

       5. associate-*l* 30.9%

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

   11. Simplified 30.9%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;y \leq 0.021:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-x \cdot a\right)\\ \end{array} \]

Alternative 12: 26.7% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-47} \lor \neg \left(y \leq 4.8 \cdot 10^{-85}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.4e-47) (not (<= y 4.8e-85))) (* a (* x (- b))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.4e-47) || !(y <= 4.8e-85)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8.4d-47)) .or. (.not. (y <= 4.8d-85))) then
        tmp = a * (x * -b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.4e-47) || !(y <= 4.8e-85)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.4e-47) or not (y <= 4.8e-85):
		tmp = a * (x * -b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.4e-47) || !(y <= 4.8e-85))
		tmp = Float64(a * Float64(x * Float64(-b)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.4e-47) || ~((y <= 4.8e-85)))
		tmp = a * (x * -b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.4e-47], N[Not[LessEqual[y, 4.8e-85]], $MachinePrecision]], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.4000000000000003e-47 or 4.8000000000000001e-85 < y

   1. Initial program 98.1%

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

   2. Taylor expanded in z around 0 98.1%

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

      1. fma-def 98.1%

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

      2. mul-1-neg 98.1%

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

      3. fma-neg 98.1%

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

      4. *-commutative 98.1%

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

   4. Simplified 98.1%

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

   5. Taylor expanded in y around 0 42.3%

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

   6. Taylor expanded in a around 0 18.0%

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

      1. +-commutative 18.0%

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

      2. mul-1-neg 18.0%

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

      3. unsub-neg 18.0%

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

   8. Simplified 18.0%

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

   9. Taylor expanded in a around inf 25.2%

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

       1. mul-1-neg 25.2%

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

       2. distribute-rgt-neg-in 25.2%

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

       3. distribute-rgt-neg-in 25.2%

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

   11. Simplified 25.2%

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

   if -8.4000000000000003e-47 < y < 4.8000000000000001e-85

   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 a around 0 58.1%

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

   3. Taylor expanded in y around 0 39.0%

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

4. Final simplification 30.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-47} \lor \neg \left(y \leq 4.8 \cdot 10^{-85}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 26.8% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-47}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.2e-47)
   (* a (* x (- b)))
   (if (<= y 3.2e-85) x (* b (- (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.2e-47) {
		tmp = a * (x * -b);
	} else if (y <= 3.2e-85) {
		tmp = x;
	} else {
		tmp = b * -(x * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8.2d-47)) then
        tmp = a * (x * -b)
    else if (y <= 3.2d-85) then
        tmp = x
    else
        tmp = b * -(x * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.2e-47) {
		tmp = a * (x * -b);
	} else if (y <= 3.2e-85) {
		tmp = x;
	} else {
		tmp = b * -(x * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.2e-47:
		tmp = a * (x * -b)
	elif y <= 3.2e-85:
		tmp = x
	else:
		tmp = b * -(x * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.2e-47)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= 3.2e-85)
		tmp = x;
	else
		tmp = Float64(b * Float64(-Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8.2e-47)
		tmp = a * (x * -b);
	elseif (y <= 3.2e-85)
		tmp = x;
	else
		tmp = b * -(x * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.2e-47], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-85], x, N[(b * (-N[(x * a), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.20000000000000003e-47

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0 98.5%

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

      1. fma-def 98.5%

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

      2. mul-1-neg 98.5%

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

      3. fma-neg 98.5%

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

      4. *-commutative 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in y around 0 38.9%

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

   6. Taylor expanded in a around 0 20.9%

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

      1. +-commutative 20.9%

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

      2. mul-1-neg 20.9%

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

      3. unsub-neg 20.9%

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

   8. Simplified 20.9%

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

   9. Taylor expanded in a around inf 26.0%

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

       1. mul-1-neg 26.0%

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

       2. distribute-rgt-neg-in 26.0%

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

       3. distribute-rgt-neg-in 26.0%

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

   11. Simplified 26.0%

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

   if -8.20000000000000003e-47 < y < 3.20000000000000027e-85

   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 a around 0 58.1%

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

   3. Taylor expanded in y around 0 39.0%

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

   if 3.20000000000000027e-85 < y

   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 z around 0 97.7%

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

      1. fma-def 97.7%

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

      2. mul-1-neg 97.7%

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

      3. fma-neg 97.7%

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

      4. *-commutative 97.7%

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

   4. Simplified 97.7%

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

   5. Taylor expanded in y around 0 44.9%

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

   6. Taylor expanded in a around 0 15.8%

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

      1. +-commutative 15.8%

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

      2. mul-1-neg 15.8%

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

      3. unsub-neg 15.8%

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

   8. Simplified 15.8%

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

   9. Taylor expanded in a around inf 24.6%

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

       1. mul-1-neg 24.6%

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

       2. associate-*r* 26.8%

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

       3. *-commutative 26.8%

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

       4. distribute-rgt-neg-out 26.8%

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

       5. associate-*l* 31.2%

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

   11. Simplified 31.2%

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

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-47}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-x \cdot a\right)\\ \end{array} \]

Alternative 14: 18.9% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in a around 0 69.6%

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

3. Taylor expanded in y around 0 19.7%

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

4. Final simplification 19.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023200 
(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))))))