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

Percentage Accurate: 96.6% → 99.6%

Time: 14.9s

Alternatives: 13

Speedup: 1.0×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% 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 95.9%

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

   1. fma-def 96.3%

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

   2. sub-neg 96.3%

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

   3. log1p-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.9%

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

2. Final simplification 95.9%

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

Alternative 3: 85.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+14} \lor \neg \left(y \leq 1.3 \cdot 10^{-50}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.8e+14) (not (<= y 1.3e-50)))
   (* 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 <= -3.8e+14) || !(y <= 1.3e-50)) {
		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 <= (-3.8d+14)) .or. (.not. (y <= 1.3d-50))) 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 <= -3.8e+14) || !(y <= 1.3e-50)) {
		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 <= -3.8e+14) or not (y <= 1.3e-50):
		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 <= -3.8e+14) || !(y <= 1.3e-50))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-Float64(z + b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.8e+14) || ~((y <= 1.3e-50)))
		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, -3.8e+14], N[Not[LessEqual[y, 1.3e-50]], $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 < -3.8e14 or 1.3000000000000001e-50 < y

   1. Initial program 99.3%

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

   2. Taylor expanded in y around inf 85.5%

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

   if -3.8e14 < y < 1.3000000000000001e-50

   1. Initial program 92.1%

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

   2. Taylor expanded in y around 0 84.2%

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

      1. sub-neg 84.2%

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

      2. neg-mul-1 84.2%

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

      3. log1p-def 92.8%

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

      4. neg-mul-1 92.8%

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

      5. sub-neg 92.8%

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

      6. +-commutative 92.8%

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

      7. +-commutative 92.8%

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

      8. sub-neg 92.8%

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

   4. Simplified 92.8%

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

   5. Taylor expanded in z around 0 92.8%

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

      1. neg-mul-1 92.8%

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

      2. unsub-neg 92.8%

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

      3. neg-mul-1 92.8%

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

   7. Simplified 92.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+14} \lor \neg \left(y \leq 1.3 \cdot 10^{-50}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \end{array} \]

Alternative 4: 76.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+15} \lor \neg \left(y \leq 1250000000\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.8e+15) (not (<= y 1250000000.0)))
   (* x (pow z y))
   (* x (exp (* a (- (+ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.8e+15) || !(y <= 1250000000.0)) {
		tmp = x * pow(z, y);
	} 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 <= (-8.8d+15)) .or. (.not. (y <= 1250000000.0d0))) then
        tmp = x * (z ** y)
    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 <= -8.8e+15) || !(y <= 1250000000.0)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((a * -(z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.8e+15) or not (y <= 1250000000.0):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((a * -(z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.8e+15) || !(y <= 1250000000.0))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-Float64(z + b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.8e+15) || ~((y <= 1250000000.0)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((a * -(z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.8e+15], N[Not[LessEqual[y, 1250000000.0]], $MachinePrecision]], N[(x * N[Power[z, y], $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 < -8.8e15 or 1.25e9 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 85.7%

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

   3. Taylor expanded in t around 0 72.2%

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

   if -8.8e15 < y < 1.25e9

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 82.5%

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

      1. sub-neg 82.5%

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

      2. neg-mul-1 82.5%

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

      3. log1p-def 90.3%

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

      4. neg-mul-1 90.3%

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

      5. sub-neg 90.3%

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

      6. +-commutative 90.3%

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

      7. +-commutative 90.3%

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

      8. sub-neg 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in z around 0 90.3%

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

      1. neg-mul-1 90.3%

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

      2. unsub-neg 90.3%

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

      3. neg-mul-1 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+15} \lor \neg \left(y \leq 1250000000\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \end{array} \]

Alternative 5: 73.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+14} \lor \neg \left(y \leq 12000000\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{-a \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.2e+14) (not (<= y 12000000.0)))
   (* x (pow z y))
   (* x (exp (- (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+14) || !(y <= 12000000.0)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp(-(a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.2d+14)) .or. (.not. (y <= 12000000.0d0))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp(-(a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+14) || !(y <= 12000000.0)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp(-(a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.2e+14) or not (y <= 12000000.0):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp(-(a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.2e+14) || !(y <= 12000000.0))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(-Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.2e+14) || ~((y <= 12000000.0)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp(-(a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.2e+14], N[Not[LessEqual[y, 12000000.0]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[(-N[(a * b), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e14 or 1.2e7 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 85.7%

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

   3. Taylor expanded in t around 0 72.2%

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

   if -3.2e14 < y < 1.2e7

   1. Initial program 92.9%

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

   2. Taylor expanded in b around inf 81.7%

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

      1. associate-*r* 81.7%

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

      2. *-commutative 81.7%

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

      3. neg-mul-1 81.7%

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

   4. Simplified 81.7%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+14} \lor \neg \left(y \leq 12000000\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{-a \cdot b}\\ \end{array} \]

Alternative 6: 59.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+14} \lor \neg \left(y \leq 4100000\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(0.5 \cdot \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right) - a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.2e+14) (not (<= y 4100000.0)))
   (* x (pow z y))
   (* x (+ 1.0 (- (* 0.5 (* (* a b) (* a b))) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+14) || !(y <= 4100000.0)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * (1.0 + ((0.5 * ((a * b) * (a * b))) - (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.2d+14)) .or. (.not. (y <= 4100000.0d0))) then
        tmp = x * (z ** y)
    else
        tmp = x * (1.0d0 + ((0.5d0 * ((a * b) * (a * b))) - (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+14) || !(y <= 4100000.0)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * (1.0 + ((0.5 * ((a * b) * (a * b))) - (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.2e+14) or not (y <= 4100000.0):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * (1.0 + ((0.5 * ((a * b) * (a * b))) - (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.2e+14) || !(y <= 4100000.0))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(0.5 * Float64(Float64(a * b) * Float64(a * b))) - Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.2e+14) || ~((y <= 4100000.0)))
		tmp = x * (z ^ y);
	else
		tmp = x * (1.0 + ((0.5 * ((a * b) * (a * b))) - (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.2e+14], N[Not[LessEqual[y, 4100000.0]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(N[(0.5 * N[(N[(a * b), $MachinePrecision] * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e14 or 4.1e6 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 85.7%

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

   3. Taylor expanded in t around 0 72.2%

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

   if -3.2e14 < y < 4.1e6

   1. Initial program 92.9%

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

      1. fma-def 92.9%

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

      2. sub-neg 92.9%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

      1. *-un-lft-identity 100.0%

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

      2. exp-prod 100.0%

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

      3. exp-1-e 100.0%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 88.3%

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

      6. sqr-neg 88.3%

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

      7. sqrt-unprod 88.3%

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

      8. add-sqr-sqrt 88.3%

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

   5. Applied egg-rr 88.3%

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

   6. Taylor expanded in b around inf 81.8%

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

      1. mul-1-neg 81.8%

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

      2. *-commutative 81.8%

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

      3. distribute-rgt-neg-in 81.8%

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

   8. Simplified 81.8%

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

   9. Taylor expanded in b around 0 54.6%

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

       1. +-commutative 54.6%

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

       2. mul-1-neg 54.6%

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

       3. unsub-neg 54.6%

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

       4. associate-*r* 54.6%

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

       5. log-E 54.6%

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

       6. metadata-eval 54.6%

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

       7. *-rgt-identity 54.6%

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

       8. unpow2 54.6%

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

       9. unpow2 54.6%

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

       10. unswap-sqr 56.9%

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

       11. log-E 56.9%

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

       12. *-rgt-identity 56.9%

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

   11. Simplified 56.9%

       \[\leadsto x \cdot \color{blue}{\left(1 + \left(0.5 \cdot \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right) - a \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+14} \lor \neg \left(y \leq 4100000\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(0.5 \cdot \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right) - a \cdot b\right)\right)\\ \end{array} \]

Alternative 7: 35.4% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 + \left(0.5 \cdot \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right) - a \cdot b\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (+ 1.0 (- (* 0.5 (* (* a b) (* a b))) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * (1.0 + ((0.5 * ((a * b) * (a * b))) - (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 * (1.0d0 + ((0.5d0 * ((a * b) * (a * b))) - (a * b)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * (1.0 + ((0.5 * ((a * b) * (a * b))) - (a * b)));
}

Python

def code(x, y, z, t, a, b):
	return x * (1.0 + ((0.5 * ((a * b) * (a * b))) - (a * b)))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * Float64(1.0 + Float64(Float64(0.5 * Float64(Float64(a * b) * Float64(a * b))) - Float64(a * b))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * (1.0 + ((0.5 * ((a * b) * (a * b))) - (a * b)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[(1.0 + N[(N[(0.5 * N[(N[(a * b), $MachinePrecision] * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.9%

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

   1. fma-def 96.3%

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

   2. sub-neg 96.3%

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

   3. log1p-def 100.0%

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

3. Simplified 100.0%

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

   1. *-un-lft-identity 100.0%

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

   2. exp-prod 100.0%

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

   3. exp-1-e 100.0%

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

   4. add-sqr-sqrt 0.0%

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

   5. sqrt-unprod 94.0%

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

   6. sqr-neg 94.0%

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

   7. sqrt-unprod 94.0%

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

   8. add-sqr-sqrt 94.0%

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

5. Applied egg-rr 94.0%

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

6. Taylor expanded in b around inf 62.5%

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

   1. mul-1-neg 62.5%

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

   2. *-commutative 62.5%

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

   3. distribute-rgt-neg-in 62.5%

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

8. Simplified 62.5%

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

9. Taylor expanded in b around 0 40.4%

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

    1. +-commutative 40.4%

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

    2. mul-1-neg 40.4%

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

    3. unsub-neg 40.4%

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

    4. associate-*r* 40.4%

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

    5. log-E 40.4%

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

    6. metadata-eval 40.4%

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

    7. *-rgt-identity 40.4%

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

    8. unpow2 40.4%

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

    9. unpow2 40.4%

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

    10. unswap-sqr 40.7%

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

    11. log-E 40.7%

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

    12. *-rgt-identity 40.7%

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

11. Simplified 40.7%

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

12. Final simplification 40.7%

    \[\leadsto x \cdot \left(1 + \left(0.5 \cdot \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right) - a \cdot b\right)\right) \]

Alternative 8: 29.7% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-185} \lor \neg \left(x \leq 1.2 \cdot 10^{-152}\right):\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.6e-185) (not (<= x 1.2e-152)))
   (* x (- 1.0 (* a b)))
   (* a (- (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.6e-185) || !(x <= 1.2e-152)) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * -(x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.6d-185)) .or. (.not. (x <= 1.2d-152))) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = a * -(x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.6e-185) || !(x <= 1.2e-152)) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * -(x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.6e-185) or not (x <= 1.2e-152):
		tmp = x * (1.0 - (a * b))
	else:
		tmp = a * -(x * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.6e-185) || !(x <= 1.2e-152))
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(a * Float64(-Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.6e-185) || ~((x <= 1.2e-152)))
		tmp = x * (1.0 - (a * b));
	else
		tmp = a * -(x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.6e-185], N[Not[LessEqual[x, 1.2e-152]], $MachinePrecision]], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * (-N[(x * z), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5999999999999999e-185 or 1.2e-152 < x

   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 b around inf 64.5%

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

      1. associate-*r* 64.5%

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

      2. *-commutative 64.5%

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

      3. neg-mul-1 64.5%

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

   4. Simplified 64.5%

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

   5. Taylor expanded in b around 0 33.4%

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

      1. mul-1-neg 33.4%

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

      2. unsub-neg 33.4%

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

      3. *-commutative 33.4%

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

   7. Simplified 33.4%

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

   if -1.5999999999999999e-185 < x < 1.2e-152

   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 y around 0 55.9%

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

      1. sub-neg 55.9%

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

      2. neg-mul-1 55.9%

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

      3. log1p-def 59.8%

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

      4. neg-mul-1 59.8%

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

      5. sub-neg 59.8%

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

      6. +-commutative 59.8%

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

      7. +-commutative 59.8%

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

      8. sub-neg 59.8%

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

   4. Simplified 59.8%

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

   5. Taylor expanded in b around 0 13.6%

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

   6. Taylor expanded in z around 0 11.4%

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

      1. mul-1-neg 11.4%

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

      2. unsub-neg 11.4%

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

   8. Simplified 11.4%

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

   9. Taylor expanded in a around inf 40.3%

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

       1. mul-1-neg 40.3%

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

       2. *-commutative 40.3%

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

       3. distribute-rgt-neg-in 40.3%

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

       4. *-commutative 40.3%

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

       5. distribute-rgt-neg-in 40.3%

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

   11. Simplified 40.3%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-185} \lor \neg \left(x \leq 1.2 \cdot 10^{-152}\right):\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-x \cdot z\right)\\ \end{array} \]

Alternative 9: 29.3% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(-x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.2e-183)
   (* x (- 1.0 (* a b)))
   (if (<= x 2.95e-106) (* a (- (* x z))) (- x (* a (* x b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.2e-183) {
		tmp = x * (1.0 - (a * b));
	} else if (x <= 2.95e-106) {
		tmp = a * -(x * z);
	} 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 <= (-6.2d-183)) then
        tmp = x * (1.0d0 - (a * b))
    else if (x <= 2.95d-106) then
        tmp = a * -(x * z)
    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 <= -6.2e-183) {
		tmp = x * (1.0 - (a * b));
	} else if (x <= 2.95e-106) {
		tmp = a * -(x * z);
	} else {
		tmp = x - (a * (x * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.2e-183:
		tmp = x * (1.0 - (a * b))
	elif x <= 2.95e-106:
		tmp = a * -(x * z)
	else:
		tmp = x - (a * (x * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.2e-183)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (x <= 2.95e-106)
		tmp = Float64(a * Float64(-Float64(x * z)));
	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 <= -6.2e-183)
		tmp = x * (1.0 - (a * b));
	elseif (x <= 2.95e-106)
		tmp = a * -(x * z);
	else
		tmp = x - (a * (x * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.2e-183], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.95e-106], N[(a * (-N[(x * z), $MachinePrecision])), $MachinePrecision], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.19999999999999999e-183

   1. Initial program 94.1%

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

   2. Taylor expanded in b around inf 69.3%

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

      1. associate-*r* 69.3%

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

      2. *-commutative 69.3%

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

      3. neg-mul-1 69.3%

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

   4. Simplified 69.3%

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

   5. Taylor expanded in b around 0 37.0%

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

      1. mul-1-neg 37.0%

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

      2. unsub-neg 37.0%

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

      3. *-commutative 37.0%

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

   7. Simplified 37.0%

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

   if -6.19999999999999999e-183 < x < 2.9499999999999999e-106

   1. Initial program 98.3%

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

   2. Taylor expanded in y around 0 53.5%

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

      1. sub-neg 53.5%

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

      2. neg-mul-1 53.5%

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

      3. log1p-def 56.9%

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

      4. neg-mul-1 56.9%

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

      5. sub-neg 56.9%

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

      6. +-commutative 56.9%

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

      7. +-commutative 56.9%

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

      8. sub-neg 56.9%

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

   4. Simplified 56.9%

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

   5. Taylor expanded in b around 0 12.1%

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

   6. Taylor expanded in z around 0 10.2%

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

      1. mul-1-neg 10.2%

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

      2. unsub-neg 10.2%

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

   8. Simplified 10.2%

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

   9. Taylor expanded in a around inf 36.6%

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

       1. mul-1-neg 36.6%

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

       2. *-commutative 36.6%

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

       3. distribute-rgt-neg-in 36.6%

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

       4. *-commutative 36.6%

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

       5. distribute-rgt-neg-in 36.6%

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

   11. Simplified 36.6%

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

   if 2.9499999999999999e-106 < x

   1. Initial program 96.6%

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

   2. Taylor expanded in b around inf 60.9%

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

      1. associate-*r* 60.9%

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

      2. *-commutative 60.9%

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

      3. neg-mul-1 60.9%

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

   4. Simplified 60.9%

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

   5. Taylor expanded in b around 0 32.8%

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

      1. +-commutative 32.8%

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

      2. mul-1-neg 32.8%

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

      3. unsub-neg 32.8%

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

   7. Simplified 32.8%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(-x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \]

Alternative 10: 23.5% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.2e+28)
   (* a (* x (- b)))
   (if (<= b 6.4e+52) x (* a (- (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.2e+28) {
		tmp = a * (x * -b);
	} else if (b <= 6.4e+52) {
		tmp = x;
	} else {
		tmp = a * -(x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.2d+28)) then
        tmp = a * (x * -b)
    else if (b <= 6.4d+52) then
        tmp = x
    else
        tmp = a * -(x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.2e+28) {
		tmp = a * (x * -b);
	} else if (b <= 6.4e+52) {
		tmp = x;
	} else {
		tmp = a * -(x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.2e+28:
		tmp = a * (x * -b)
	elif b <= 6.4e+52:
		tmp = x
	else:
		tmp = a * -(x * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.2e+28)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (b <= 6.4e+52)
		tmp = x;
	else
		tmp = Float64(a * Float64(-Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.2e+28)
		tmp = a * (x * -b);
	elseif (b <= 6.4e+52)
		tmp = x;
	else
		tmp = a * -(x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.2e+28], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.4e+52], x, N[(a * (-N[(x * z), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.2000000000000001e28

   1. Initial program 98.2%

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

   2. Taylor expanded in b around inf 85.9%

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

      1. associate-*r* 85.9%

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

      2. *-commutative 85.9%

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

      3. neg-mul-1 85.9%

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

   4. Simplified 85.9%

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

   5. Taylor expanded in b around 0 41.7%

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

      1. mul-1-neg 41.7%

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

      2. unsub-neg 41.7%

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

      3. *-commutative 41.7%

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

   7. Simplified 41.7%

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

   8. Taylor expanded in b around inf 35.4%

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

      1. mul-1-neg 35.4%

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

      2. distribute-rgt-neg-in 35.4%

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

      3. distribute-rgt-neg-in 35.4%

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

   10. Simplified 35.4%

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

   if -6.2000000000000001e28 < b < 6.4e52

   1. Initial program 93.7%

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

   2. Taylor expanded in b around inf 48.5%

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

      1. associate-*r* 48.5%

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

      2. *-commutative 48.5%

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

      3. neg-mul-1 48.5%

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

   4. Simplified 48.5%

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

   5. Taylor expanded in b around 0 28.5%

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

   if 6.4e52 < b

   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 0 76.9%

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

      1. sub-neg 76.9%

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

      2. neg-mul-1 76.9%

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

      3. log1p-def 76.9%

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

      4. neg-mul-1 76.9%

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

      5. sub-neg 76.9%

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

      6. +-commutative 76.9%

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

      7. +-commutative 76.9%

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

      8. sub-neg 76.9%

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

   4. Simplified 76.9%

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

   5. Taylor expanded in b around 0 11.6%

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

   6. Taylor expanded in z around 0 9.7%

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

      1. mul-1-neg 9.7%

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

      2. unsub-neg 9.7%

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

   8. Simplified 9.7%

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

   9. Taylor expanded in a around inf 23.5%

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

       1. mul-1-neg 23.5%

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

       2. *-commutative 23.5%

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

       3. distribute-rgt-neg-in 23.5%

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

       4. *-commutative 23.5%

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

       5. distribute-rgt-neg-in 23.5%

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

   11. Simplified 23.5%

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

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-x \cdot z\right)\\ \end{array} \]

Alternative 11: 23.8% accurate, 34.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+132} \lor \neg \left(y \leq 2.7 \cdot 10^{+59}\right):\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.9e+132) (not (<= y 2.7e+59))) (* a (* x b)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.9e+132) || !(y <= 2.7e+59)) {
		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 <= (-3.9d+132)) .or. (.not. (y <= 2.7d+59))) 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 <= -3.9e+132) || !(y <= 2.7e+59)) {
		tmp = a * (x * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.9e+132) or not (y <= 2.7e+59):
		tmp = a * (x * b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.9e+132) || !(y <= 2.7e+59))
		tmp = Float64(a * Float64(x * b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.9e+132) || ~((y <= 2.7e+59)))
		tmp = a * (x * b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.9e+132], N[Not[LessEqual[y, 2.7e+59]], $MachinePrecision]], N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.90000000000000001e132 or 2.7000000000000001e59 < y

   1. Initial program 98.7%

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

   2. Taylor expanded in b around inf 46.3%

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

      1. associate-*r* 46.3%

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

      2. *-commutative 46.3%

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

      3. neg-mul-1 46.3%

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

   4. Simplified 46.3%

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

   5. Taylor expanded in b 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%

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

      3. *-commutative 14.3%

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

   7. Simplified 14.3%

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

   8. Taylor expanded in b around inf 20.3%

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

      1. mul-1-neg 20.3%

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

      2. distribute-rgt-neg-in 20.3%

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

      3. distribute-rgt-neg-in 20.3%

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

   10. Simplified 20.3%

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

       1. expm1-log1p-u 16.9%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(b \cdot \left(-x\right)\right)\right)\right)} \]

       2. expm1-udef 29.7%

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

       3. associate-*r* 32.2%

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

       4. add-sqr-sqrt 13.4%

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

       5. *-commutative 13.4%

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

       6. sqrt-unprod 25.8%

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

       7. sqr-neg 25.8%

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

       8. sqrt-unprod 13.7%

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

       9. add-sqr-sqrt 27.1%

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

       10. associate-*r* 27.1%

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

   12. Applied egg-rr 27.1%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(b \cdot \left(a \cdot x\right)\right)} - 1} \]
   13. Step-by-step derivation

       1. expm1-def 14.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(a \cdot x\right)\right)\right)} \]

       2. expm1-log1p 18.6%

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

       3. associate-*r* 17.4%

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

       4. *-commutative 17.4%

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

       5. associate-*r* 19.9%

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

   14. Simplified 19.9%

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

   if -3.90000000000000001e132 < y < 2.7000000000000001e59

   1. Initial program 94.8%

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

   2. Taylor expanded in b around inf 69.3%

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

      1. associate-*r* 69.3%

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

      2. *-commutative 69.3%

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

      3. neg-mul-1 69.3%

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

   4. Simplified 69.3%

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

   5. Taylor expanded in b around 0 26.9%

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

4. Final simplification 24.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+132} \lor \neg \left(y \leq 2.7 \cdot 10^{+59}\right):\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 21.6% accurate, 39.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.1e+28) (* a (* x (- b))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.1e+28) {
		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 (b <= (-2.1d+28)) 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 (b <= -2.1e+28) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.1e+28:
		tmp = a * (x * -b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.1e+28)
		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 (b <= -2.1e+28)
		tmp = a * (x * -b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.1e+28], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -2.09999999999999989e28

   1. Initial program 98.2%

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

   2. Taylor expanded in b around inf 85.9%

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

      1. associate-*r* 85.9%

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

      2. *-commutative 85.9%

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

      3. neg-mul-1 85.9%

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

   4. Simplified 85.9%

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

   5. Taylor expanded in b around 0 41.7%

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

      1. mul-1-neg 41.7%

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

      2. unsub-neg 41.7%

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

      3. *-commutative 41.7%

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

   7. Simplified 41.7%

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

   8. Taylor expanded in b around inf 35.4%

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

      1. mul-1-neg 35.4%

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

      2. distribute-rgt-neg-in 35.4%

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

      3. distribute-rgt-neg-in 35.4%

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

   10. Simplified 35.4%

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

   if -2.09999999999999989e28 < b

   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 b around inf 55.8%

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

      1. associate-*r* 55.8%

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

      2. *-commutative 55.8%

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

      3. neg-mul-1 55.8%

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

   4. Simplified 55.8%

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

   5. Taylor expanded in b around 0 23.6%

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

4. Final simplification 26.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 19.8% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.9%

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

2. Taylor expanded in b around inf 62.5%

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

   1. associate-*r* 62.5%

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

   2. *-commutative 62.5%

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

   3. neg-mul-1 62.5%

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

4. Simplified 62.5%

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

5. Taylor expanded in b around 0 20.0%

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

6. Final simplification 20.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023171 
(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))))))