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

Percentage Accurate: 96.6% → 99.6%

Time: 18.6s

Alternatives: 16

Speedup: 1.0×

• 41.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.6% 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 96.5%

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

   1. fma-define 96.5%

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

   2. sub-neg 96.5%

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

   3. log1p-define 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. Add Preprocessing

5. Final simplification 100.0%

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

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 96.5%

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

3. Final simplification 96.5%

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

Alternative 3: 87.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-14} \lor \neg \left(y \leq 1.65 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.1e-14) (not (<= y 1.65e-26)))
   (* 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 <= -2.1e-14) || !(y <= 1.65e-26)) {
		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 <= (-2.1d-14)) .or. (.not. (y <= 1.65d-26))) 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 <= -2.1e-14) || !(y <= 1.65e-26)) {
		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 <= -2.1e-14) or not (y <= 1.65e-26):
		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 <= -2.1e-14) || !(y <= 1.65e-26))
		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 <= -2.1e-14) || ~((y <= 1.65e-26)))
		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, -2.1e-14], N[Not[LessEqual[y, 1.65e-26]], $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 < -2.0999999999999999e-14 or 1.6499999999999999e-26 < y

   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. Step-by-step derivation

      1. fma-define 97.2%

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

      2. sub-neg 97.2%

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

      3. log1p-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 95.1%

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

   if -2.0999999999999999e-14 < y < 1.6499999999999999e-26

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0 84.9%

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

      1. sub-neg 84.9%

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

      2. log1p-define 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in z around 0 89.1%

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

      1. associate-*r* 89.1%

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

      2. associate-*r* 89.1%

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

      3. distribute-lft-out 89.1%

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

      4. mul-1-neg 89.1%

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

   8. Simplified 89.1%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-14} \lor \neg \left(y \leq 1.65 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -0.0076:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-15}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+155} \lor \neg \left(y \leq 2 \cdot 10^{+262}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -0.0076)
     t_1
     (if (<= y 6.2e-15)
       (* x (exp (* (- a) (+ z b))))
       (if (or (<= y 1.85e+155) (not (<= y 2e+262)))
         t_1
         (* x (exp (* t (- y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -0.0076) {
		tmp = t_1;
	} else if (y <= 6.2e-15) {
		tmp = x * exp((-a * (z + b)));
	} else if ((y <= 1.85e+155) || !(y <= 2e+262)) {
		tmp = t_1;
	} else {
		tmp = x * exp((t * -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) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-0.0076d0)) then
        tmp = t_1
    else if (y <= 6.2d-15) then
        tmp = x * exp((-a * (z + b)))
    else if ((y <= 1.85d+155) .or. (.not. (y <= 2d+262))) then
        tmp = t_1
    else
        tmp = x * exp((t * -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 t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -0.0076) {
		tmp = t_1;
	} else if (y <= 6.2e-15) {
		tmp = x * Math.exp((-a * (z + b)));
	} else if ((y <= 1.85e+155) || !(y <= 2e+262)) {
		tmp = t_1;
	} else {
		tmp = x * Math.exp((t * -y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -0.0076:
		tmp = t_1
	elif y <= 6.2e-15:
		tmp = x * math.exp((-a * (z + b)))
	elif (y <= 1.85e+155) or not (y <= 2e+262):
		tmp = t_1
	else:
		tmp = x * math.exp((t * -y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -0.0076)
		tmp = t_1;
	elseif (y <= 6.2e-15)
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	elseif ((y <= 1.85e+155) || !(y <= 2e+262))
		tmp = t_1;
	else
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -0.0076)
		tmp = t_1;
	elseif (y <= 6.2e-15)
		tmp = x * exp((-a * (z + b)));
	elseif ((y <= 1.85e+155) || ~((y <= 2e+262)))
		tmp = t_1;
	else
		tmp = x * exp((t * -y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0076], t$95$1, If[LessEqual[y, 6.2e-15], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.85e+155], N[Not[LessEqual[y, 2e+262]], $MachinePrecision]], t$95$1, N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00759999999999999998 or 6.1999999999999998e-15 < y < 1.8499999999999999e155 or 2e262 < 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. Step-by-step derivation

      1. fma-define 97.4%

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

      2. sub-neg 97.4%

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

      3. log1p-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 94.9%

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

   6. Taylor expanded in t around 0 76.3%

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

   if -0.00759999999999999998 < y < 6.1999999999999998e-15

   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. Add Preprocessing

   3. Taylor expanded in y around 0 84.5%

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

      1. sub-neg 84.5%

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

      2. log1p-define 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in z around 0 88.6%

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

      1. associate-*r* 88.6%

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

      2. associate-*r* 88.6%

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

      3. distribute-lft-out 88.6%

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

      4. mul-1-neg 88.6%

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

   8. Simplified 88.6%

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

   if 1.8499999999999999e155 < y < 2e262

   1. Initial program 95.5%

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

      1. fma-define 95.5%

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

      2. sub-neg 95.5%

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

      3. log1p-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 95.5%

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

   6. Taylor expanded in t around inf 73.5%

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

      1. neg-mul-1 73.5%

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

   8. Simplified 73.5%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0076:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-15}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+155} \lor \neg \left(y \leq 2 \cdot 10^{+262}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-69}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-28}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* t (- y))))))
   (if (<= t -3.1e+22)
     t_1
     (if (<= t -4.8e-69)
       (* x (exp (* a (- b))))
       (if (<= t 3e-28) (* x (pow z y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((t * -y));
	double tmp;
	if (t <= -3.1e+22) {
		tmp = t_1;
	} else if (t <= -4.8e-69) {
		tmp = x * exp((a * -b));
	} else if (t <= 3e-28) {
		tmp = x * pow(z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * exp((t * -y))
    if (t <= (-3.1d+22)) then
        tmp = t_1
    else if (t <= (-4.8d-69)) then
        tmp = x * exp((a * -b))
    else if (t <= 3d-28) then
        tmp = x * (z ** y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((t * -y));
	double tmp;
	if (t <= -3.1e+22) {
		tmp = t_1;
	} else if (t <= -4.8e-69) {
		tmp = x * Math.exp((a * -b));
	} else if (t <= 3e-28) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((t * -y))
	tmp = 0
	if t <= -3.1e+22:
		tmp = t_1
	elif t <= -4.8e-69:
		tmp = x * math.exp((a * -b))
	elif t <= 3e-28:
		tmp = x * math.pow(z, y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(t * Float64(-y))))
	tmp = 0.0
	if (t <= -3.1e+22)
		tmp = t_1;
	elseif (t <= -4.8e-69)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif (t <= 3e-28)
		tmp = Float64(x * (z ^ y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((t * -y));
	tmp = 0.0;
	if (t <= -3.1e+22)
		tmp = t_1;
	elseif (t <= -4.8e-69)
		tmp = x * exp((a * -b));
	elseif (t <= 3e-28)
		tmp = x * (z ^ y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+22], t$95$1, If[LessEqual[t, -4.8e-69], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-28], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.1000000000000002e22 or 3.00000000000000003e-28 < t

   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. Step-by-step derivation

      1. fma-define 99.2%

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

      2. sub-neg 99.2%

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

      3. log1p-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 79.9%

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

   6. Taylor expanded in t around inf 79.9%

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

      1. neg-mul-1 79.9%

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

   8. Simplified 79.9%

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

   if -3.1000000000000002e22 < t < -4.8000000000000002e-69

   1. Initial program 89.0%

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

   3. Taylor expanded in b around inf 78.2%

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

      1. mul-1-neg 78.2%

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

      2. distribute-rgt-neg-out 78.2%

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

   5. Simplified 78.2%

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

   if -4.8000000000000002e-69 < t < 3.00000000000000003e-28

   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. Step-by-step derivation

      1. fma-define 94.8%

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

      2. sub-neg 94.8%

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

      3. log1p-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 77.0%

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

   6. Taylor expanded in t around 0 77.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+22}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-69}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-28}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \lor \neg \left(y \leq 6.2 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.02) (not (<= y 6.2e-15)))
   (* 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 <= -1.02) || !(y <= 6.2e-15)) {
		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 <= (-1.02d0)) .or. (.not. (y <= 6.2d-15))) 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 <= -1.02) || !(y <= 6.2e-15)) {
		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 <= -1.02) or not (y <= 6.2e-15):
		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 <= -1.02) || !(y <= 6.2e-15))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.02) || ~((y <= 6.2e-15)))
		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, -1.02], N[Not[LessEqual[y, 6.2e-15]], $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 < -1.02 or 6.1999999999999998e-15 < y

   1. Initial program 97.1%

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

      1. fma-define 97.1%

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

      2. sub-neg 97.1%

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

      3. log1p-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 95.0%

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

   6. Taylor expanded in t around 0 72.9%

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

   if -1.02 < y < 6.1999999999999998e-15

   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. Add Preprocessing

   3. Taylor expanded in b around inf 82.8%

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

      1. mul-1-neg 82.8%

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

      2. distribute-rgt-neg-out 82.8%

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

   5. Simplified 82.8%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \lor \neg \left(y \leq 6.2 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.3e-6) (* x (- 1.0 (* y t))) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.3e-6) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.3d-6)) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.3e-6) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.3e-6:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.3e-6)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.3e-6)
		tmp = x * (1.0 - (y * t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.3e-6], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.30000000000000005e-6

   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. Step-by-step derivation

      1. fma-define 98.5%

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

      2. sub-neg 98.5%

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

      3. log1p-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 81.0%

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

   6. Taylor expanded in t around inf 82.5%

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

      1. neg-mul-1 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in y around 0 35.9%

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

       1. associate-*r* 35.9%

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

       2. mul-1-neg 35.9%

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

       3. cancel-sign-sub-inv 35.9%

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

   11. Simplified 35.9%

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

   if -1.30000000000000005e-6 < t

   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-define 95.9%

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

      2. sub-neg 95.9%

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

      3. log1p-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 74.8%

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

   6. Taylor expanded in t around 0 69.7%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 30.6% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(\frac{x}{z} - x \cdot a\right)\\ \mathbf{elif}\;a \leq 98000000:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.8e+14)
   (* z (- (/ x z) (* x a)))
   (if (<= a 98000000.0)
     (* x (- 1.0 (* y t)))
     (if (<= a 4.9e+89) (* a (* z (- x))) (- x (* x (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.8e+14) {
		tmp = z * ((x / z) - (x * a));
	} else if (a <= 98000000.0) {
		tmp = x * (1.0 - (y * t));
	} else if (a <= 4.9e+89) {
		tmp = a * (z * -x);
	} else {
		tmp = x - (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 (a <= (-6.8d+14)) then
        tmp = z * ((x / z) - (x * a))
    else if (a <= 98000000.0d0) then
        tmp = x * (1.0d0 - (y * t))
    else if (a <= 4.9d+89) then
        tmp = a * (z * -x)
    else
        tmp = x - (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 (a <= -6.8e+14) {
		tmp = z * ((x / z) - (x * a));
	} else if (a <= 98000000.0) {
		tmp = x * (1.0 - (y * t));
	} else if (a <= 4.9e+89) {
		tmp = a * (z * -x);
	} else {
		tmp = x - (x * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.8e+14:
		tmp = z * ((x / z) - (x * a))
	elif a <= 98000000.0:
		tmp = x * (1.0 - (y * t))
	elif a <= 4.9e+89:
		tmp = a * (z * -x)
	else:
		tmp = x - (x * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.8e+14)
		tmp = Float64(z * Float64(Float64(x / z) - Float64(x * a)));
	elseif (a <= 98000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif (a <= 4.9e+89)
		tmp = Float64(a * Float64(z * Float64(-x)));
	else
		tmp = Float64(x - Float64(x * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6.8e+14)
		tmp = z * ((x / z) - (x * a));
	elseif (a <= 98000000.0)
		tmp = x * (1.0 - (y * t));
	elseif (a <= 4.9e+89)
		tmp = a * (z * -x);
	else
		tmp = x - (x * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.8e+14], N[(z * N[(N[(x / z), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 98000000.0], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e+89], N[(a * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.8e14

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 75.2%

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

      1. sub-neg 75.2%

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

      2. log1p-define 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in b around 0 9.9%

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

   7. Taylor expanded in z around 0 14.5%

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

      1. mul-1-neg 14.5%

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

      2. unsub-neg 14.5%

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

      3. *-commutative 14.5%

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

   9. Simplified 14.5%

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

   10. Taylor expanded in z around inf 27.9%

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

   if -6.8e14 < a < 9.8e7

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 90.4%

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

   6. Taylor expanded in t around inf 72.8%

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

      1. neg-mul-1 72.8%

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

   8. Simplified 72.8%

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

   9. Taylor expanded in y around 0 44.6%

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

       1. associate-*r* 44.6%

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

       2. mul-1-neg 44.6%

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

       3. cancel-sign-sub-inv 44.6%

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

   11. Simplified 44.6%

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

   if 9.8e7 < a < 4.89999999999999996e89

   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. Add Preprocessing

   3. Taylor expanded in y around 0 72.2%

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

      1. sub-neg 72.2%

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

      2. log1p-define 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in b around 0 13.2%

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

   7. Taylor expanded in z around 0 7.1%

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

      1. mul-1-neg 7.1%

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

      2. unsub-neg 7.1%

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

      3. *-commutative 7.1%

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

   9. Simplified 7.1%

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

   10. Taylor expanded in z around inf 33.2%

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

       1. associate-*r* 33.2%

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

       2. neg-mul-1 33.2%

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

   12. Simplified 33.2%

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

   if 4.89999999999999996e89 < a

   1. Initial program 87.8%

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

   3. Taylor expanded in b around inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. distribute-rgt-neg-out 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in a around 0 27.4%

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

      1. mul-1-neg 27.4%

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

      2. unsub-neg 27.4%

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

      3. *-commutative 27.4%

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

   8. Simplified 27.4%

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

   9. Taylor expanded in a around 0 27.4%

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

       1. associate-*r* 36.6%

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

       2. *-commutative 36.6%

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

   11. Simplified 36.6%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(\frac{x}{z} - x \cdot a\right)\\ \mathbf{elif}\;a \leq 98000000:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 25.6% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-41} \lor \neg \left(y \leq 7 \cdot 10^{-137}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e-41) (not (<= y 7e-137))) (* z (* x (- a))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e-41) || !(y <= 7e-137)) {
		tmp = z * (x * -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.7d-41)) .or. (.not. (y <= 7d-137))) then
        tmp = z * (x * -a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e-41) || !(y <= 7e-137)) {
		tmp = z * (x * -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.7e-41) or not (y <= 7e-137):
		tmp = z * (x * -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.7e-41) || !(y <= 7e-137))
		tmp = Float64(z * Float64(x * Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.7e-41) || ~((y <= 7e-137)))
		tmp = z * (x * -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.7e-41], N[Not[LessEqual[y, 7e-137]], $MachinePrecision]], N[(z * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e-41 or 7.0000000000000002e-137 < y

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0 43.3%

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

      1. sub-neg 43.3%

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

      2. log1p-define 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in b around 0 6.5%

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

   7. Taylor expanded in z around 0 7.3%

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

      1. mul-1-neg 7.3%

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

      2. unsub-neg 7.3%

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

      3. *-commutative 7.3%

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

   9. Simplified 7.3%

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

   10. Taylor expanded in z around inf 21.7%

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

       1. mul-1-neg 21.7%

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

       2. *-commutative 21.7%

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

       3. *-commutative 21.7%

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

       4. associate-*r* 19.6%

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

   12. Simplified 19.6%

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

   if -2.7e-41 < y < 7.0000000000000002e-137

   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. Add Preprocessing

   3. Taylor expanded in b around inf 83.9%

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

      1. mul-1-neg 83.9%

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

      2. distribute-rgt-neg-out 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in a around 0 43.0%

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

4. Final simplification 27.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-41} \lor \neg \left(y \leq 7 \cdot 10^{-137}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 28.0% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.4e-41)
   (* z (* x (- a)))
   (if (<= y 7.2e-58) x (* x (* z (- a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.4e-41) {
		tmp = z * (x * -a);
	} else if (y <= 7.2e-58) {
		tmp = x;
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.4d-41)) then
        tmp = z * (x * -a)
    else if (y <= 7.2d-58) then
        tmp = x
    else
        tmp = x * (z * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.4e-41) {
		tmp = z * (x * -a);
	} else if (y <= 7.2e-58) {
		tmp = x;
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.4e-41:
		tmp = z * (x * -a)
	elif y <= 7.2e-58:
		tmp = x
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.4e-41)
		tmp = Float64(z * Float64(x * Float64(-a)));
	elseif (y <= 7.2e-58)
		tmp = x;
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.4e-41)
		tmp = z * (x * -a);
	elseif (y <= 7.2e-58)
		tmp = x;
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.4e-41], N[(z * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-58], x, N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3999999999999998e-41

   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. Add Preprocessing

   3. Taylor expanded in y around 0 38.9%

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

      1. sub-neg 38.9%

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

      2. log1p-define 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in b around 0 4.6%

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

   7. Taylor expanded in z around 0 5.1%

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

      1. mul-1-neg 5.1%

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

      2. unsub-neg 5.1%

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

      3. *-commutative 5.1%

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

   9. Simplified 5.1%

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

   10. Taylor expanded in z around inf 12.8%

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

       1. mul-1-neg 12.8%

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

       2. *-commutative 12.8%

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

       3. *-commutative 12.8%

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

       4. associate-*r* 14.0%

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

   12. Simplified 14.0%

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

   if -3.3999999999999998e-41 < y < 7.20000000000000019e-58

   1. Initial program 97.1%

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

   3. Taylor expanded in b around inf 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-rgt-neg-out 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in a around 0 40.2%

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

   if 7.20000000000000019e-58 < y

   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. Add Preprocessing

   3. Taylor expanded in y around 0 41.6%

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

      1. sub-neg 41.6%

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

      2. log1p-define 43.0%

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

   5. Simplified 43.0%

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

   6. Taylor expanded in b around 0 6.1%

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

   7. Taylor expanded in z around 0 7.3%

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

      1. mul-1-neg 7.3%

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

      2. unsub-neg 7.3%

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

      3. *-commutative 7.3%

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

   9. Simplified 7.3%

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

   10. Taylor expanded in z around inf 28.1%

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

       1. associate-*r* 28.1%

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

       2. neg-mul-1 28.1%

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

       3. *-commutative 28.1%

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

   12. Simplified 28.1%

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

4. Final simplification 28.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 26.4% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.02e-39)
   (* z (* x (- a)))
   (if (<= y 1.05e-137) x (* a (* z (- x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.02e-39) {
		tmp = z * (x * -a);
	} else if (y <= 1.05e-137) {
		tmp = x;
	} else {
		tmp = a * (z * -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 <= (-1.02d-39)) then
        tmp = z * (x * -a)
    else if (y <= 1.05d-137) then
        tmp = x
    else
        tmp = a * (z * -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 <= -1.02e-39) {
		tmp = z * (x * -a);
	} else if (y <= 1.05e-137) {
		tmp = x;
	} else {
		tmp = a * (z * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.02e-39:
		tmp = z * (x * -a)
	elif y <= 1.05e-137:
		tmp = x
	else:
		tmp = a * (z * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.02e-39)
		tmp = Float64(z * Float64(x * Float64(-a)));
	elseif (y <= 1.05e-137)
		tmp = x;
	else
		tmp = Float64(a * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.02e-39)
		tmp = z * (x * -a);
	elseif (y <= 1.05e-137)
		tmp = x;
	else
		tmp = a * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.02e-39], N[(z * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-137], x, N[(a * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.02000000000000007e-39

   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. Add Preprocessing

   3. Taylor expanded in y around 0 38.9%

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

      1. sub-neg 38.9%

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

      2. log1p-define 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in b around 0 4.6%

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

   7. Taylor expanded in z around 0 5.1%

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

      1. mul-1-neg 5.1%

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

      2. unsub-neg 5.1%

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

      3. *-commutative 5.1%

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

   9. Simplified 5.1%

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

   10. Taylor expanded in z around inf 12.8%

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

       1. mul-1-neg 12.8%

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

       2. *-commutative 12.8%

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

       3. *-commutative 12.8%

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

       4. associate-*r* 14.0%

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

   12. Simplified 14.0%

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

   if -1.02000000000000007e-39 < y < 1.04999999999999996e-137

   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. Add Preprocessing

   3. Taylor expanded in b around inf 84.8%

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

      1. mul-1-neg 84.8%

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

      2. distribute-rgt-neg-out 84.8%

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

   5. Simplified 84.8%

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

   6. Taylor expanded in a around 0 43.4%

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

   if 1.04999999999999996e-137 < y

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0 47.2%

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

      1. sub-neg 47.2%

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

      2. log1p-define 49.4%

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

   5. Simplified 49.4%

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

   6. Taylor expanded in b around 0 8.5%

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

   7. Taylor expanded in z around 0 9.4%

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

      1. mul-1-neg 9.4%

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

      2. unsub-neg 9.4%

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

      3. *-commutative 9.4%

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

   9. Simplified 9.4%

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

   10. Taylor expanded in z around inf 31.5%

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

       1. associate-*r* 31.5%

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

       2. neg-mul-1 31.5%

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

   12. Simplified 31.5%

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

4. Final simplification 29.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 24.9% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{-159}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 7e-159) (* a (* z (- x))) (* x (- 1.0 (* y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 7e-159) {
		tmp = a * (z * -x);
	} else {
		tmp = x * (1.0 - (y * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 7d-159) then
        tmp = a * (z * -x)
    else
        tmp = x * (1.0d0 - (y * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 7e-159) {
		tmp = a * (z * -x);
	} else {
		tmp = x * (1.0 - (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 7e-159:
		tmp = a * (z * -x)
	else:
		tmp = x * (1.0 - (y * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 7e-159)
		tmp = Float64(a * Float64(z * Float64(-x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 7e-159)
		tmp = a * (z * -x);
	else
		tmp = x * (1.0 - (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 7e-159], N[(a * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.00000000000000005e-159

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0 55.8%

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

      1. sub-neg 55.8%

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

      2. log1p-define 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in b around 0 18.2%

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

   7. Taylor expanded in z around 0 19.1%

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

      1. mul-1-neg 19.1%

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

      2. unsub-neg 19.1%

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

      3. *-commutative 19.1%

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

   9. Simplified 19.1%

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

   10. Taylor expanded in z around inf 22.7%

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

       1. associate-*r* 22.7%

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

       2. neg-mul-1 22.7%

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

   12. Simplified 22.7%

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

   if 7.00000000000000005e-159 < x

   1. Initial program 96.7%

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

      1. fma-define 96.7%

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

      2. sub-neg 96.7%

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

      3. log1p-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 72.2%

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

   6. Taylor expanded in t around inf 54.9%

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

      1. neg-mul-1 54.9%

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

   8. Simplified 54.9%

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

   9. Taylor expanded in y around 0 30.2%

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

       1. associate-*r* 30.2%

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

       2. mul-1-neg 30.2%

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

       3. cancel-sign-sub-inv 30.2%

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

   11. Simplified 30.2%

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

4. Final simplification 25.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{-159}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 24.9% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.5 \cdot 10^{-158}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 5.5e-158) (* 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 <= 5.5e-158) {
		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 <= 5.5d-158) 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 <= 5.5e-158) {
		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 <= 5.5e-158:
		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 <= 5.5e-158)
		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 <= 5.5e-158)
		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, 5.5e-158], 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 < 5.50000000000000025e-158

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0 55.8%

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

      1. sub-neg 55.8%

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

      2. log1p-define 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in b around 0 18.2%

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

   7. Taylor expanded in z around 0 19.1%

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

      1. mul-1-neg 19.1%

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

      2. unsub-neg 19.1%

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

      3. *-commutative 19.1%

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

   9. Simplified 19.1%

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

   10. Taylor expanded in z around inf 22.7%

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

       1. associate-*r* 22.7%

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

       2. neg-mul-1 22.7%

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

   12. Simplified 22.7%

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

   if 5.50000000000000025e-158 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. distribute-rgt-neg-out 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in a around 0 27.2%

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

      1. mul-1-neg 27.2%

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

      2. unsub-neg 27.2%

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

      3. *-commutative 27.2%

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

   8. Simplified 27.2%

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

4. Final simplification 24.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.5 \cdot 10^{-158}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.2% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{-155}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 2.5e-155) (* a (* z (- x))) (- x (* b (* x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.5e-155) {
		tmp = a * (z * -x);
	} else {
		tmp = x - (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 2.5d-155) then
        tmp = a * (z * -x)
    else
        tmp = x - (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.5e-155) {
		tmp = a * (z * -x);
	} else {
		tmp = x - (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 2.5e-155:
		tmp = a * (z * -x)
	else:
		tmp = x - (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 2.5e-155)
		tmp = Float64(a * Float64(z * Float64(-x)));
	else
		tmp = Float64(x - Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 2.5e-155)
		tmp = a * (z * -x);
	else
		tmp = x - (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 2.5e-155], N[(a * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.4999999999999999e-155

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0 55.8%

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

      1. sub-neg 55.8%

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

      2. log1p-define 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in b around 0 18.2%

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

   7. Taylor expanded in z around 0 19.1%

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

      1. mul-1-neg 19.1%

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

      2. unsub-neg 19.1%

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

      3. *-commutative 19.1%

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

   9. Simplified 19.1%

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

   10. Taylor expanded in z around inf 22.7%

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

       1. associate-*r* 22.7%

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

       2. neg-mul-1 22.7%

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

   12. Simplified 22.7%

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

   if 2.4999999999999999e-155 < x

   1. Initial program 96.7%

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

      1. fma-define 96.7%

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

      2. sub-neg 96.7%

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

      3. log1p-define 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. Add Preprocessing
   5. Step-by-step derivation

      1. add-sqr-sqrt 99.9%

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

      2. pow2 99.9%

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

   6. Applied egg-rr 93.3%

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

   7. Taylor expanded in b around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. distribute-rgt-neg-in 59.0%

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

   9. Simplified 59.0%

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

   10. Taylor expanded in a around 0 27.2%

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

       1. mul-1-neg 27.2%

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

       2. unsub-neg 27.2%

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

       3. *-commutative 27.2%

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

       4. associate-*l* 30.5%

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

   12. Simplified 30.5%

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

4. Final simplification 25.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{-155}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 25.0% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.5 \cdot 10^{-160}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 5.5e-160) (* a (* z (- x))) (- x (* x (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 5.5e-160) {
		tmp = a * (z * -x);
	} else {
		tmp = x - (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 (x <= 5.5d-160) then
        tmp = a * (z * -x)
    else
        tmp = x - (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 (x <= 5.5e-160) {
		tmp = a * (z * -x);
	} else {
		tmp = x - (x * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 5.5e-160:
		tmp = a * (z * -x)
	else:
		tmp = x - (x * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 5.5e-160)
		tmp = Float64(a * Float64(z * Float64(-x)));
	else
		tmp = Float64(x - Float64(x * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 5.5e-160)
		tmp = a * (z * -x);
	else
		tmp = x - (x * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 5.5e-160], N[(a * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.5e-160

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0 55.8%

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

      1. sub-neg 55.8%

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

      2. log1p-define 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in b around 0 18.2%

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

   7. Taylor expanded in z around 0 19.1%

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

      1. mul-1-neg 19.1%

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

      2. unsub-neg 19.1%

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

      3. *-commutative 19.1%

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

   9. Simplified 19.1%

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

   10. Taylor expanded in z around inf 22.7%

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

       1. associate-*r* 22.7%

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

       2. neg-mul-1 22.7%

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

   12. Simplified 22.7%

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

   if 5.5e-160 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. distribute-rgt-neg-out 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in a around 0 27.2%

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

      1. mul-1-neg 27.2%

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

      2. unsub-neg 27.2%

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

      3. *-commutative 27.2%

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

   8. Simplified 27.2%

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

   9. Taylor expanded in a around 0 27.2%

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

       1. associate-*r* 29.4%

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

       2. *-commutative 29.4%

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

   11. Simplified 29.4%

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

4. Final simplification 25.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.5 \cdot 10^{-160}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 19.4% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in b around inf 56.9%

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

   1. mul-1-neg 56.9%

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

   2. distribute-rgt-neg-out 56.9%

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

5. Simplified 56.9%

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

6. Taylor expanded in a around 0 18.4%

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

7. Final simplification 18.4%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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))))))