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

Percentage Accurate: 96.4% → 99.4%

Time: 14.3s

Alternatives: 15

Speedup: 1.0×

• 41.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.4% 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: 99.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. fma-def 98.1%

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

   2. sub-neg 98.1%

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

   3. log1p-def 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+64} \lor \neg \left(b \leq 1.2 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \mathsf{log1p}\left(-z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.75e+64) (not (<= b 1.2e+82)))
   (* x (exp (* a (- b))))
   (* x (exp (+ (* y (- (log z) t)) (* a (log1p (- z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.75e+64) || !(b <= 1.2e+82)) {
		tmp = x * exp((a * -b));
	} else {
		tmp = x * exp(((y * (log(z) - t)) + (a * log1p(-z))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.75e+64) || !(b <= 1.2e+82)) {
		tmp = x * Math.exp((a * -b));
	} else {
		tmp = x * Math.exp(((y * (Math.log(z) - t)) + (a * Math.log1p(-z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.75e+64) or not (b <= 1.2e+82):
		tmp = x * math.exp((a * -b))
	else:
		tmp = x * math.exp(((y * (math.log(z) - t)) + (a * math.log1p(-z))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.75e+64) || !(b <= 1.2e+82))
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	else
		tmp = Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * log1p(Float64(-z))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.75e+64], N[Not[LessEqual[b, 1.2e+82]], $MachinePrecision]], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[Log[1 + (-z)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7499999999999999e64 or 1.19999999999999999e82 < b

   1. Initial program 98.0%

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

   2. Taylor expanded in b around inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. distribute-rgt-neg-out 85.4%

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

   4. Simplified 85.4%

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

   if -1.7499999999999999e64 < b < 1.19999999999999999e82

   1. Initial program 97.4%

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

   2. Taylor expanded in b around 0 86.8%

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

      1. sub-neg 86.8%

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

      2. neg-mul-1 86.8%

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

      3. log1p-def 90.5%

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

      4. neg-mul-1 90.5%

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

   4. Simplified 90.5%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right) + \color{blue}{a \cdot \mathsf{log1p}\left(-z\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+64} \lor \neg \left(b \leq 1.2 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \mathsf{log1p}\left(-z\right)}\\ \end{array} \]

Alternative 3: 96.4% 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]

Derivation

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. Final simplification 97.7%

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

Alternative 4: 87.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-72} \lor \neg \left(y \leq 3.4 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8e-72) (not (<= y 3.4e+15)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (log1p (- z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e-72) || !(y <= 3.4e+15)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * (log1p(-z) - b)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e-72) || !(y <= 3.4e+15)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * (Math.log1p(-z) - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8e-72) or not (y <= 3.4e+15):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * (math.log1p(-z) - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8e-72) || !(y <= 3.4e+15))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(log1p(Float64(-z)) - b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8e-72], N[Not[LessEqual[y, 3.4e+15]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[(N[Log[1 + (-z)], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.9999999999999997e-72 or 3.4e15 < y

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf 84.7%

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

   if -7.9999999999999997e-72 < y < 3.4e15

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0 83.4%

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

      1. sub-neg 83.4%

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

      2. sub-neg 83.4%

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

      3. neg-mul-1 83.4%

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

      4. log1p-def 85.1%

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

      5. neg-mul-1 85.1%

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

      6. sub-neg 85.1%

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

   4. Simplified 85.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-72} \lor \neg \left(y \leq 3.4 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}\\ \end{array} \]

Alternative 5: 86.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-71} \lor \neg \left(y \leq 3.1 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.55e-71) (not (<= y 3.1e+22)))
   (* 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 <= -2.55e-71) || !(y <= 3.1e+22)) {
		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 <= (-2.55d-71)) .or. (.not. (y <= 3.1d+22))) 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 <= -2.55e-71) || !(y <= 3.1e+22)) {
		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 <= -2.55e-71) or not (y <= 3.1e+22):
		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 <= -2.55e-71) || !(y <= 3.1e+22))
		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 <= -2.55e-71) || ~((y <= 3.1e+22)))
		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, -2.55e-71], N[Not[LessEqual[y, 3.1e+22]], $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 < -2.5500000000000001e-71 or 3.1000000000000002e22 < y

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf 84.7%

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

   if -2.5500000000000001e-71 < y < 3.1000000000000002e22

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0 83.4%

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

      1. sub-neg 83.4%

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

      2. sub-neg 83.4%

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

      3. neg-mul-1 83.4%

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

      4. log1p-def 85.1%

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

      5. neg-mul-1 85.1%

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

      6. sub-neg 85.1%

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

   4. Simplified 85.1%

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

   5. Taylor expanded in z around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-*r* 85.1%

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

      3. associate-*r* 85.1%

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

      4. distribute-lft-out 85.1%

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

      5. neg-mul-1 85.1%

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

   7. Simplified 85.1%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-71} \lor \neg \left(y \leq 3.1 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]

Alternative 6: 73.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ t_2 := x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-60}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* (- a) (+ z b))))) (t_2 (* x (exp (* y (- t))))))
   (if (<= t -6.5e+114)
     t_2
     (if (<= t 8.5e-230)
       t_1
       (if (<= t 2.8e-60) (* x (pow z y)) (if (<= t 2.5e+128) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((-a * (z + b)));
	double t_2 = x * exp((y * -t));
	double tmp;
	if (t <= -6.5e+114) {
		tmp = t_2;
	} else if (t <= 8.5e-230) {
		tmp = t_1;
	} else if (t <= 2.8e-60) {
		tmp = x * pow(z, y);
	} else if (t <= 2.5e+128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 * exp((-a * (z + b)))
    t_2 = x * exp((y * -t))
    if (t <= (-6.5d+114)) then
        tmp = t_2
    else if (t <= 8.5d-230) then
        tmp = t_1
    else if (t <= 2.8d-60) then
        tmp = x * (z ** y)
    else if (t <= 2.5d+128) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((-a * (z + b)));
	double t_2 = x * Math.exp((y * -t));
	double tmp;
	if (t <= -6.5e+114) {
		tmp = t_2;
	} else if (t <= 8.5e-230) {
		tmp = t_1;
	} else if (t <= 2.8e-60) {
		tmp = x * Math.pow(z, y);
	} else if (t <= 2.5e+128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((-a * (z + b)))
	t_2 = x * math.exp((y * -t))
	tmp = 0
	if t <= -6.5e+114:
		tmp = t_2
	elif t <= 8.5e-230:
		tmp = t_1
	elif t <= 2.8e-60:
		tmp = x * math.pow(z, y)
	elif t <= 2.5e+128:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))))
	t_2 = Float64(x * exp(Float64(y * Float64(-t))))
	tmp = 0.0
	if (t <= -6.5e+114)
		tmp = t_2;
	elseif (t <= 8.5e-230)
		tmp = t_1;
	elseif (t <= 2.8e-60)
		tmp = Float64(x * (z ^ y));
	elseif (t <= 2.5e+128)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((-a * (z + b)));
	t_2 = x * exp((y * -t));
	tmp = 0.0;
	if (t <= -6.5e+114)
		tmp = t_2;
	elseif (t <= 8.5e-230)
		tmp = t_1;
	elseif (t <= 2.8e-60)
		tmp = x * (z ^ y);
	elseif (t <= 2.5e+128)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+114], t$95$2, If[LessEqual[t, 8.5e-230], t$95$1, If[LessEqual[t, 2.8e-60], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+128], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5000000000000001e114 or 2.5e128 < t

   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 t around inf 88.5%

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

      1. mul-1-neg 88.5%

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

      2. *-commutative 88.5%

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

   4. Simplified 88.5%

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

   if -6.5000000000000001e114 < t < 8.4999999999999998e-230 or 2.8000000000000002e-60 < t < 2.5e128

   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. Taylor expanded in y around 0 73.9%

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

      1. sub-neg 73.9%

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

      2. sub-neg 73.9%

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

      3. neg-mul-1 73.9%

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

      4. log1p-def 75.8%

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

      5. neg-mul-1 75.8%

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

      6. sub-neg 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in z around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-*r* 75.8%

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

      3. associate-*r* 75.8%

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

      4. distribute-lft-out 75.8%

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

      5. neg-mul-1 75.8%

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

   7. Simplified 75.8%

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

   if 8.4999999999999998e-230 < t < 2.8000000000000002e-60

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 84.3%

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

   3. Taylor expanded in t around 0 84.3%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+114}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-230}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-60}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+128}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 7: 70.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{a \cdot \left(-b\right)}\\ t_2 := x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-61}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* a (- b))))) (t_2 (* x (exp (* y (- t))))))
   (if (<= t -9.2e+117)
     t_2
     (if (<= t 9.5e-231)
       t_1
       (if (<= t 9.5e-61) (* x (pow z y)) (if (<= t 2.25e+128) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((a * -b));
	double t_2 = x * exp((y * -t));
	double tmp;
	if (t <= -9.2e+117) {
		tmp = t_2;
	} else if (t <= 9.5e-231) {
		tmp = t_1;
	} else if (t <= 9.5e-61) {
		tmp = x * pow(z, y);
	} else if (t <= 2.25e+128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 * exp((a * -b))
    t_2 = x * exp((y * -t))
    if (t <= (-9.2d+117)) then
        tmp = t_2
    else if (t <= 9.5d-231) then
        tmp = t_1
    else if (t <= 9.5d-61) then
        tmp = x * (z ** y)
    else if (t <= 2.25d+128) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((a * -b));
	double t_2 = x * Math.exp((y * -t));
	double tmp;
	if (t <= -9.2e+117) {
		tmp = t_2;
	} else if (t <= 9.5e-231) {
		tmp = t_1;
	} else if (t <= 9.5e-61) {
		tmp = x * Math.pow(z, y);
	} else if (t <= 2.25e+128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((a * -b))
	t_2 = x * math.exp((y * -t))
	tmp = 0
	if t <= -9.2e+117:
		tmp = t_2
	elif t <= 9.5e-231:
		tmp = t_1
	elif t <= 9.5e-61:
		tmp = x * math.pow(z, y)
	elif t <= 2.25e+128:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(a * Float64(-b))))
	t_2 = Float64(x * exp(Float64(y * Float64(-t))))
	tmp = 0.0
	if (t <= -9.2e+117)
		tmp = t_2;
	elseif (t <= 9.5e-231)
		tmp = t_1;
	elseif (t <= 9.5e-61)
		tmp = Float64(x * (z ^ y));
	elseif (t <= 2.25e+128)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((a * -b));
	t_2 = x * exp((y * -t));
	tmp = 0.0;
	if (t <= -9.2e+117)
		tmp = t_2;
	elseif (t <= 9.5e-231)
		tmp = t_1;
	elseif (t <= 9.5e-61)
		tmp = x * (z ^ y);
	elseif (t <= 2.25e+128)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+117], t$95$2, If[LessEqual[t, 9.5e-231], t$95$1, If[LessEqual[t, 9.5e-61], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e+128], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.19999999999999951e117 or 2.2500000000000001e128 < t

   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 t around inf 88.5%

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

      1. mul-1-neg 88.5%

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

      2. *-commutative 88.5%

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

   4. Simplified 88.5%

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

   if -9.19999999999999951e117 < t < 9.4999999999999995e-231 or 9.49999999999999986e-61 < t < 2.2500000000000001e128

   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. Taylor expanded in b around inf 72.6%

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

      1. mul-1-neg 72.6%

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

      2. distribute-rgt-neg-out 72.6%

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

   4. Simplified 72.6%

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

   if 9.4999999999999995e-231 < t < 9.49999999999999986e-61

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 84.3%

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

   3. Taylor expanded in t around 0 84.3%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+117}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-61}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+128}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 8: 72.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-13} \lor \neg \left(t \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.9e-13) (not (<= t 5e-9)))
   (* 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 <= -2.9e-13) || !(t <= 5e-9)) {
		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 <= (-2.9d-13)) .or. (.not. (t <= 5d-9))) 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 <= -2.9e-13) || !(t <= 5e-9)) {
		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 <= -2.9e-13) or not (t <= 5e-9):
		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 <= -2.9e-13) || !(t <= 5e-9))
		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 <= -2.9e-13) || ~((t <= 5e-9)))
		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, -2.9e-13], N[Not[LessEqual[t, 5e-9]], $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 < -2.8999999999999998e-13 or 5.0000000000000001e-9 < t

   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 t around inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. *-commutative 77.1%

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

   4. Simplified 77.1%

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

   if -2.8999999999999998e-13 < t < 5.0000000000000001e-9

   1. Initial program 98.2%

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

   2. Taylor expanded in y around inf 61.9%

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

   3. Taylor expanded in t around 0 61.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-13} \lor \neg \left(t \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 9: 54.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8e+116) (* x (* a (- b))) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8e+116) {
		tmp = x * (a * -b);
	} 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 <= (-8d+116)) then
        tmp = x * (a * -b)
    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 <= -8e+116) {
		tmp = x * (a * -b);
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -8e+116:
		tmp = x * (a * -b)
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8e+116)
		tmp = Float64(x * Float64(a * Float64(-b)));
	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 <= -8e+116)
		tmp = x * (a * -b);
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8e+116], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.00000000000000012e116

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 31.9%

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

      1. mul-1-neg 31.9%

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

      2. distribute-rgt-neg-out 31.9%

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

   4. Simplified 31.9%

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

   5. Taylor expanded in a around 0 14.3%

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

      1. mul-1-neg 14.3%

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

      2. unsub-neg 14.3%

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

   7. Simplified 14.3%

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

   8. Taylor expanded in a around inf 22.9%

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

      1. mul-1-neg 22.9%

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

      2. associate-*r* 25.0%

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

      3. *-commutative 25.0%

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

      4. distribute-lft-neg-in 25.0%

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

   10. Simplified 25.0%

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

   if -8.00000000000000012e116 < t

   1. Initial program 97.2%

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

   2. Taylor expanded in y around inf 65.8%

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

   3. Taylor expanded in t around 0 56.7%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 10: 27.0% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00055 \lor \neg \left(y \leq 1.9 \cdot 10^{-119}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.00055) (not (<= y 1.9e-119))) (* a (* x (- b))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.00055) || !(y <= 1.9e-119)) {
		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 <= (-0.00055d0)) .or. (.not. (y <= 1.9d-119))) 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 <= -0.00055) || !(y <= 1.9e-119)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -0.00055) or not (y <= 1.9e-119):
		tmp = a * (x * -b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -0.00055) || !(y <= 1.9e-119))
		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 <= -0.00055) || ~((y <= 1.9e-119)))
		tmp = a * (x * -b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -0.00055], N[Not[LessEqual[y, 1.9e-119]], $MachinePrecision]], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000033e-4 or 1.89999999999999987e-119 < y

   1. Initial program 97.4%

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

   2. Taylor expanded in b around inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. distribute-rgt-neg-out 44.8%

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

   4. Simplified 44.8%

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

   5. Taylor expanded in a around 0 12.7%

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

      1. mul-1-neg 12.7%

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

      2. unsub-neg 12.7%

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

   7. Simplified 12.7%

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

   8. Taylor expanded in a around inf 24.1%

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

      1. mul-1-neg 24.1%

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

      2. *-commutative 24.1%

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

      3. distribute-rgt-neg-in 24.1%

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

      4. distribute-rgt-neg-in 24.1%

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

   10. Simplified 24.1%

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

   if -5.50000000000000033e-4 < y < 1.89999999999999987e-119

   1. Initial program 98.0%

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

   2. Taylor expanded in b around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. distribute-rgt-neg-out 78.9%

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

   4. Simplified 78.9%

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

   5. Taylor expanded in a around 0 31.7%

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

4. Final simplification 27.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00055 \lor \neg \left(y \leq 1.9 \cdot 10^{-119}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 25.9% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.9 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.9e-48)
   (* x (* z (- a)))
   (if (<= y 1.9e-119) x (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.9e-48) {
		tmp = x * (z * -a);
	} else if (y <= 1.9e-119) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8.9d-48)) then
        tmp = x * (z * -a)
    else if (y <= 1.9d-119) then
        tmp = x
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.9e-48) {
		tmp = x * (z * -a);
	} else if (y <= 1.9e-119) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.9e-48:
		tmp = x * (z * -a)
	elif y <= 1.9e-119:
		tmp = x
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.9e-48)
		tmp = Float64(x * Float64(z * Float64(-a)));
	elseif (y <= 1.9e-119)
		tmp = x;
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8.9e-48)
		tmp = x * (z * -a);
	elseif (y <= 1.9e-119)
		tmp = x;
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.9e-48], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-119], x, N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.90000000000000014e-48

   1. Initial program 97.5%

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

   2. Taylor expanded in b around 0 85.6%

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

      1. sub-neg 85.6%

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

      2. neg-mul-1 85.6%

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

      3. log1p-def 86.8%

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

      4. neg-mul-1 86.8%

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

   4. Simplified 86.8%

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

   5. Taylor expanded in y around 0 6.1%

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

   6. Taylor expanded in z around 0 4.4%

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

      1. mul-1-neg 4.4%

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

      2. unsub-neg 4.4%

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

      3. *-commutative 4.4%

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

      4. associate-*l* 4.4%

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

      5. *-commutative 4.4%

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

   8. Simplified 4.4%

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

   9. Taylor expanded in a around inf 13.1%

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

       1. mul-1-neg 13.1%

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

       2. *-commutative 13.1%

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

       3. associate-*r* 15.4%

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

       4. distribute-rgt-neg-out 15.4%

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

       5. *-commutative 15.4%

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

       6. distribute-rgt-neg-in 15.4%

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

   11. Simplified 15.4%

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

   if -8.90000000000000014e-48 < y < 1.89999999999999987e-119

   1. Initial program 97.8%

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

   2. Taylor expanded in b around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. distribute-rgt-neg-out 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in a around 0 35.1%

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

   if 1.89999999999999987e-119 < 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 b around inf 48.4%

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

      1. mul-1-neg 48.4%

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

      2. distribute-rgt-neg-out 48.4%

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

   4. Simplified 48.4%

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

   5. Taylor expanded in a around 0 17.8%

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

      1. mul-1-neg 17.8%

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

      2. unsub-neg 17.8%

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

   7. Simplified 17.8%

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

   8. Taylor expanded in a around inf 31.1%

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

      1. mul-1-neg 31.1%

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

      2. *-commutative 31.1%

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

      3. distribute-rgt-neg-in 31.1%

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

      4. distribute-rgt-neg-in 31.1%

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

   10. Simplified 31.1%

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

4. Final simplification 27.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.9 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 12: 26.2% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.35e-47)
   (* x (* z (- a)))
   (if (<= y 1.9e-119) x (* x (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.35e-47) {
		tmp = x * (z * -a);
	} else if (y <= 1.9e-119) {
		tmp = x;
	} else {
		tmp = x * (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 <= (-1.35d-47)) then
        tmp = x * (z * -a)
    else if (y <= 1.9d-119) then
        tmp = x
    else
        tmp = x * (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 <= -1.35e-47) {
		tmp = x * (z * -a);
	} else if (y <= 1.9e-119) {
		tmp = x;
	} else {
		tmp = x * (a * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.35e-47:
		tmp = x * (z * -a)
	elif y <= 1.9e-119:
		tmp = x
	else:
		tmp = x * (a * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.35e-47)
		tmp = Float64(x * Float64(z * Float64(-a)));
	elseif (y <= 1.9e-119)
		tmp = x;
	else
		tmp = Float64(x * Float64(a * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.35e-47)
		tmp = x * (z * -a);
	elseif (y <= 1.9e-119)
		tmp = x;
	else
		tmp = x * (a * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.35e-47], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-119], x, N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3499999999999999e-47

   1. Initial program 97.5%

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

   2. Taylor expanded in b around 0 85.6%

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

      1. sub-neg 85.6%

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

      2. neg-mul-1 85.6%

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

      3. log1p-def 86.8%

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

      4. neg-mul-1 86.8%

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

   4. Simplified 86.8%

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

   5. Taylor expanded in y around 0 6.1%

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

   6. Taylor expanded in z around 0 4.4%

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

      1. mul-1-neg 4.4%

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

      2. unsub-neg 4.4%

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

      3. *-commutative 4.4%

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

      4. associate-*l* 4.4%

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

      5. *-commutative 4.4%

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

   8. Simplified 4.4%

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

   9. Taylor expanded in a around inf 13.1%

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

       1. mul-1-neg 13.1%

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

       2. *-commutative 13.1%

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

       3. associate-*r* 15.4%

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

       4. distribute-rgt-neg-out 15.4%

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

       5. *-commutative 15.4%

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

       6. distribute-rgt-neg-in 15.4%

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

   11. Simplified 15.4%

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

   if -1.3499999999999999e-47 < y < 1.89999999999999987e-119

   1. Initial program 97.8%

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

   2. Taylor expanded in b around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. distribute-rgt-neg-out 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in a around 0 35.1%

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

   if 1.89999999999999987e-119 < 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 b around inf 48.4%

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

      1. mul-1-neg 48.4%

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

      2. distribute-rgt-neg-out 48.4%

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

   4. Simplified 48.4%

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

   5. Taylor expanded in a around 0 17.8%

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

      1. mul-1-neg 17.8%

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

      2. unsub-neg 17.8%

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

   7. Simplified 17.8%

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

   8. Taylor expanded in a around inf 31.1%

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

      1. mul-1-neg 31.1%

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

      2. associate-*r* 31.2%

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

      3. *-commutative 31.2%

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

      4. distribute-lft-neg-in 31.2%

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

   10. Simplified 31.2%

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

4. Final simplification 27.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 13: 24.8% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 2.8e-45) (* a (* z (- x))) (* x (- 1.0 (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.8e-45) {
		tmp = a * (z * -x);
	} 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 (x <= 2.8d-45) then
        tmp = a * (z * -x)
    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 (x <= 2.8e-45) {
		tmp = a * (z * -x);
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 2.8e-45:
		tmp = a * (z * -x)
	else:
		tmp = x * (1.0 - (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 2.8e-45)
		tmp = Float64(a * Float64(z * Float64(-x)));
	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 (x <= 2.8e-45)
		tmp = a * (z * -x);
	else
		tmp = x * (1.0 - (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 2.8e-45], N[(a * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.8000000000000001e-45

   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 b around 0 70.3%

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

      1. sub-neg 70.3%

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

      2. neg-mul-1 70.3%

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

      3. log1p-def 75.2%

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

      4. neg-mul-1 75.2%

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

   4. Simplified 75.2%

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

   5. Taylor expanded in y around 0 15.9%

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

   6. Taylor expanded in z around 0 13.2%

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

      1. mul-1-neg 13.2%

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

      2. unsub-neg 13.2%

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

      3. *-commutative 13.2%

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

      4. associate-*l* 13.2%

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

      5. *-commutative 13.2%

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

   8. Simplified 13.2%

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

   9. Taylor expanded in a around inf 21.2%

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

   if 2.8000000000000001e-45 < x

   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 b around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-rgt-neg-out 53.4%

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

   4. Simplified 53.4%

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

   5. Taylor expanded in a around 0 34.1%

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

      1. mul-1-neg 34.1%

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

      2. unsub-neg 34.1%

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

   7. Simplified 34.1%

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

4. Final simplification 24.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \]

Alternative 14: 25.0% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.8 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 3.8e-45) (* a (* z (- x))) (- x (* a (* x b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 3.8e-45) {
		tmp = a * (z * -x);
	} else {
		tmp = x - (a * (x * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 3.8d-45) then
        tmp = a * (z * -x)
    else
        tmp = x - (a * (x * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 3.8e-45) {
		tmp = a * (z * -x);
	} else {
		tmp = x - (a * (x * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 3.8e-45:
		tmp = a * (z * -x)
	else:
		tmp = x - (a * (x * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 3.8e-45)
		tmp = Float64(a * Float64(z * Float64(-x)));
	else
		tmp = Float64(x - Float64(a * Float64(x * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 3.8e-45)
		tmp = a * (z * -x);
	else
		tmp = x - (a * (x * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 3.8e-45], N[(a * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.79999999999999997e-45

   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 b around 0 70.3%

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

      1. sub-neg 70.3%

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

      2. neg-mul-1 70.3%

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

      3. log1p-def 75.2%

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

      4. neg-mul-1 75.2%

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

   4. Simplified 75.2%

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

   5. Taylor expanded in y around 0 15.9%

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

   6. Taylor expanded in z around 0 13.2%

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

      1. mul-1-neg 13.2%

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

      2. unsub-neg 13.2%

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

      3. *-commutative 13.2%

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

      4. associate-*l* 13.2%

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

      5. *-commutative 13.2%

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

   8. Simplified 13.2%

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

   9. Taylor expanded in a around inf 21.2%

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

   if 3.79999999999999997e-45 < x

   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 b around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-rgt-neg-out 53.4%

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

   4. Simplified 53.4%

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

   5. Taylor expanded in a around 0 32.5%

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

      1. mul-1-neg 32.5%

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

      2. unsub-neg 32.5%

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

      3. *-commutative 32.5%

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

   7. Simplified 32.5%

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

4. Final simplification 23.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.8 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \]

Alternative 15: 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 97.7%

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

2. Taylor expanded in b around inf 58.4%

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

   1. mul-1-neg 58.4%

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

   2. distribute-rgt-neg-out 58.4%

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

4. Simplified 58.4%

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

5. Taylor expanded in a around 0 15.7%

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

6. Final simplification 15.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023334 
(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))))))