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

Percentage Accurate: 96.6% → 99.6%

Time: 20.1s

Alternatives: 18

Speedup: 1.0×

• 20.6% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Step-by-step derivation

   1. +-commutative 95.4%

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

   2. fma-def 96.2%

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

   3. sub-neg 96.2%

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

   4. log1p-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.4%

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

2. Final simplification 95.4%

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

Alternative 3: 87.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -48000000000000 \lor \neg \left(y \leq 8.4 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{-a \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -48000000000000.0) (not (<= y 8.4e-35)))
   (* 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 <= -48000000000000.0) || !(y <= 8.4e-35)) {
		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 <= (-48000000000000.0d0)) .or. (.not. (y <= 8.4d-35))) 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 <= -48000000000000.0) || !(y <= 8.4e-35)) {
		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 <= -48000000000000.0) or not (y <= 8.4e-35):
		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 <= -48000000000000.0) || !(y <= 8.4e-35))
		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 <= -48000000000000.0) || ~((y <= 8.4e-35)))
		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, -48000000000000.0], N[Not[LessEqual[y, 8.4e-35]], $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 < -4.8e13 or 8.3999999999999999e-35 < y

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf 91.7%

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

   if -4.8e13 < y < 8.3999999999999999e-35

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0 81.9%

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

      1. sub-neg 81.9%

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

      2. neg-mul-1 81.9%

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

      3. log1p-def 87.2%

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

      4. neg-mul-1 87.2%

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

      5. sub-neg 87.2%

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

      6. sub-neg 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in z around 0 87.2%

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

      1. associate-*r* 87.2%

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

      2. associate-*r* 87.2%

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

      3. distribute-lft-out 87.2%

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

      4. neg-mul-1 87.2%

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

   7. Simplified 87.2%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -48000000000000 \lor \neg \left(y \leq 8.4 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{-a \cdot \left(z + b\right)}\\ \end{array} \]

Alternative 4: 70.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{t \cdot \left(-y\right)}\\ t_2 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -66000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+191} \lor \neg \left(y \leq 2 \cdot 10^{+248}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* t (- y))))) (t_2 (* x (pow z y))))
   (if (<= y -1.55e+171)
     t_2
     (if (<= y -7.5e+87)
       t_1
       (if (<= y -66000000000000.0)
         t_2
         (if (<= y 5.2e-33)
           (* x (exp (* a (- b))))
           (if (or (<= y 5.5e+191) (not (<= y 2e+248))) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((t * -y));
	double t_2 = x * pow(z, y);
	double tmp;
	if (y <= -1.55e+171) {
		tmp = t_2;
	} else if (y <= -7.5e+87) {
		tmp = t_1;
	} else if (y <= -66000000000000.0) {
		tmp = t_2;
	} else if (y <= 5.2e-33) {
		tmp = x * exp((a * -b));
	} else if ((y <= 5.5e+191) || !(y <= 2e+248)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * exp((t * -y))
    t_2 = x * (z ** y)
    if (y <= (-1.55d+171)) then
        tmp = t_2
    else if (y <= (-7.5d+87)) then
        tmp = t_1
    else if (y <= (-66000000000000.0d0)) then
        tmp = t_2
    else if (y <= 5.2d-33) then
        tmp = x * exp((a * -b))
    else if ((y <= 5.5d+191) .or. (.not. (y <= 2d+248))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((t * -y));
	double t_2 = x * Math.pow(z, y);
	double tmp;
	if (y <= -1.55e+171) {
		tmp = t_2;
	} else if (y <= -7.5e+87) {
		tmp = t_1;
	} else if (y <= -66000000000000.0) {
		tmp = t_2;
	} else if (y <= 5.2e-33) {
		tmp = x * Math.exp((a * -b));
	} else if ((y <= 5.5e+191) || !(y <= 2e+248)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((t * -y))
	t_2 = x * math.pow(z, y)
	tmp = 0
	if y <= -1.55e+171:
		tmp = t_2
	elif y <= -7.5e+87:
		tmp = t_1
	elif y <= -66000000000000.0:
		tmp = t_2
	elif y <= 5.2e-33:
		tmp = x * math.exp((a * -b))
	elif (y <= 5.5e+191) or not (y <= 2e+248):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(t * Float64(-y))))
	t_2 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -1.55e+171)
		tmp = t_2;
	elseif (y <= -7.5e+87)
		tmp = t_1;
	elseif (y <= -66000000000000.0)
		tmp = t_2;
	elseif (y <= 5.2e-33)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif ((y <= 5.5e+191) || !(y <= 2e+248))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((t * -y));
	t_2 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -1.55e+171)
		tmp = t_2;
	elseif (y <= -7.5e+87)
		tmp = t_1;
	elseif (y <= -66000000000000.0)
		tmp = t_2;
	elseif (y <= 5.2e-33)
		tmp = x * exp((a * -b));
	elseif ((y <= 5.5e+191) || ~((y <= 2e+248)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+171], t$95$2, If[LessEqual[y, -7.5e+87], t$95$1, If[LessEqual[y, -66000000000000.0], t$95$2, If[LessEqual[y, 5.2e-33], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 5.5e+191], N[Not[LessEqual[y, 2e+248]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5499999999999999e171 or -7.50000000000000014e87 < y < -6.6e13 or 5.5000000000000002e191 < y < 2.00000000000000009e248

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 88.4%

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

   3. Taylor expanded in t around 0 78.8%

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

   if -1.5499999999999999e171 < y < -7.50000000000000014e87 or 5.19999999999999988e-33 < y < 5.5000000000000002e191 or 2.00000000000000009e248 < y

   1. Initial program 95.0%

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

   2. Taylor expanded in t around inf 79.4%

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

      1. mul-1-neg 79.4%

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

      2. distribute-rgt-neg-in 79.4%

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

   4. Simplified 79.4%

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

   if -6.6e13 < y < 5.19999999999999988e-33

   1. Initial program 94.7%

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

   2. Taylor expanded in b around inf 81.9%

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

      1. associate-*r* 81.9%

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

      2. *-commutative 81.9%

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

      3. neg-mul-1 81.9%

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

   4. Simplified 81.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+171}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+87}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq -66000000000000:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+191} \lor \neg \left(y \leq 2 \cdot 10^{+248}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 5: 72.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3800:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+125} \lor \neg \left(y \leq 5 \cdot 10^{+194}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot y\right)\right) \cdot \left(t \cdot \left(t \cdot 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -9e+14)
     t_1
     (if (<= y 3800.0)
       (* x (exp (* a (- b))))
       (if (or (<= y 7.6e+125) (not (<= y 5e+194)))
         t_1
         (* (* x (* y y)) (* t (* t 0.5))))))))

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 <= -9e+14) {
		tmp = t_1;
	} else if (y <= 3800.0) {
		tmp = x * exp((a * -b));
	} else if ((y <= 7.6e+125) || !(y <= 5e+194)) {
		tmp = t_1;
	} else {
		tmp = (x * (y * y)) * (t * (t * 0.5));
	}
	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 <= (-9d+14)) then
        tmp = t_1
    else if (y <= 3800.0d0) then
        tmp = x * exp((a * -b))
    else if ((y <= 7.6d+125) .or. (.not. (y <= 5d+194))) then
        tmp = t_1
    else
        tmp = (x * (y * y)) * (t * (t * 0.5d0))
    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 <= -9e+14) {
		tmp = t_1;
	} else if (y <= 3800.0) {
		tmp = x * Math.exp((a * -b));
	} else if ((y <= 7.6e+125) || !(y <= 5e+194)) {
		tmp = t_1;
	} else {
		tmp = (x * (y * y)) * (t * (t * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -9e+14:
		tmp = t_1
	elif y <= 3800.0:
		tmp = x * math.exp((a * -b))
	elif (y <= 7.6e+125) or not (y <= 5e+194):
		tmp = t_1
	else:
		tmp = (x * (y * y)) * (t * (t * 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -9e+14)
		tmp = t_1;
	elseif (y <= 3800.0)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif ((y <= 7.6e+125) || !(y <= 5e+194))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(y * y)) * Float64(t * Float64(t * 0.5)));
	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 <= -9e+14)
		tmp = t_1;
	elseif (y <= 3800.0)
		tmp = x * exp((a * -b));
	elseif ((y <= 7.6e+125) || ~((y <= 5e+194)))
		tmp = t_1;
	else
		tmp = (x * (y * y)) * (t * (t * 0.5));
	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, -9e+14], t$95$1, If[LessEqual[y, 3800.0], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 7.6e+125], N[Not[LessEqual[y, 5e+194]], $MachinePrecision]], t$95$1, N[(N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision] * N[(t * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9e14 or 3800 < y < 7.60000000000000003e125 or 4.99999999999999989e194 < 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. Taylor expanded in y around inf 92.2%

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

   3. Taylor expanded in t around 0 66.0%

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

   if -9e14 < y < 3800

   1. Initial program 94.9%

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

   2. Taylor expanded in b around inf 80.4%

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

      1. associate-*r* 80.4%

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

      2. *-commutative 80.4%

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

      3. neg-mul-1 80.4%

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

   4. Simplified 80.4%

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

   if 7.60000000000000003e125 < y < 4.99999999999999989e194

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. distribute-rgt-neg-in 84.9%

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

   4. Simplified 84.9%

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

   5. Taylor expanded in t around 0 77.2%

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-1 \cdot \left(t \cdot y\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 77.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -1 \cdot \left(t \cdot y\right)\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)} \]

      2. mul-1-neg 77.2%

         \[\leadsto x \cdot \left(\left(1 + \color{blue}{\left(-t \cdot y\right)}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      3. unsub-neg 77.2%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - t \cdot y\right)} + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      4. *-commutative 77.2%

         \[\leadsto x \cdot \left(\left(1 - \color{blue}{y \cdot t}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      5. associate-*r* 77.2%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + \color{blue}{\left(0.5 \cdot {t}^{2}\right) \cdot {y}^{2}}\right) \]

      6. unpow2 77.2%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + \left(0.5 \cdot \color{blue}{\left(t \cdot t\right)}\right) \cdot {y}^{2}\right) \]

      7. unpow2 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in y around inf 77.2%

      \[\leadsto \color{blue}{0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. unpow2 77.2%

         \[\leadsto 0.5 \cdot \left(\color{blue}{\left(t \cdot t\right)} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      2. associate-*r* 77.2%

         \[\leadsto \color{blue}{\left(0.5 \cdot \left(t \cdot t\right)\right) \cdot \left(x \cdot {y}^{2}\right)} \]

      3. *-commutative 77.2%

         \[\leadsto \color{blue}{\left(x \cdot {y}^{2}\right) \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)} \]

      4. unpow2 77.2%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot y\right)}\right) \cdot \left(0.5 \cdot \left(t \cdot t\right)\right) \]

      5. associate-*r* 77.2%

         \[\leadsto \left(x \cdot \left(y \cdot y\right)\right) \cdot \color{blue}{\left(\left(0.5 \cdot t\right) \cdot t\right)} \]

      6. *-commutative 77.2%

         \[\leadsto \left(x \cdot \left(y \cdot y\right)\right) \cdot \color{blue}{\left(t \cdot \left(0.5 \cdot t\right)\right)} \]

   10. Simplified 77.2%

       \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot y\right)\right) \cdot \left(t \cdot \left(0.5 \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+14}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 3800:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+125} \lor \neg \left(y \leq 5 \cdot 10^{+194}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot y\right)\right) \cdot \left(t \cdot \left(t \cdot 0.5\right)\right)\\ \end{array} \]

Alternative 6: 75.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+42} \lor \neg \left(t \leq 2.5 \cdot 10^{+45}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{-a \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.2e+42) (not (<= t 2.5e+45)))
   (* x (exp (* t (- y))))
   (* x (exp (- (* a (+ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.2e+42) || !(t <= 2.5e+45)) {
		tmp = x * exp((t * -y));
	} else {
		tmp = x * exp(-(a * (z + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.2d+42)) .or. (.not. (t <= 2.5d+45))) then
        tmp = x * exp((t * -y))
    else
        tmp = x * exp(-(a * (z + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.2e+42) || !(t <= 2.5e+45)) {
		tmp = x * Math.exp((t * -y));
	} else {
		tmp = x * Math.exp(-(a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.2e+42) or not (t <= 2.5e+45):
		tmp = x * math.exp((t * -y))
	else:
		tmp = x * math.exp(-(a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.2e+42) || !(t <= 2.5e+45))
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	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 ((t <= -1.2e+42) || ~((t <= 2.5e+45)))
		tmp = x * exp((t * -y));
	else
		tmp = x * exp(-(a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.2e+42], N[Not[LessEqual[t, 2.5e+45]], $MachinePrecision]], N[(x * N[Exp[N[(t * (-y)), $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 t < -1.1999999999999999e42 or 2.5e45 < t

   1. Initial program 94.9%

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

   2. Taylor expanded in t around inf 81.8%

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

      1. mul-1-neg 81.8%

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

      2. distribute-rgt-neg-in 81.8%

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

   4. Simplified 81.8%

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

   if -1.1999999999999999e42 < t < 2.5e45

   1. Initial program 95.9%

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

   2. Taylor expanded in y around 0 67.5%

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

      1. sub-neg 67.5%

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

      2. neg-mul-1 67.5%

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

      3. log1p-def 72.8%

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

      4. neg-mul-1 72.8%

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

      5. sub-neg 72.8%

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

      6. sub-neg 72.8%

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

   4. Simplified 72.8%

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

   5. Taylor expanded in z around 0 72.8%

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

      1. associate-*r* 72.8%

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

      2. associate-*r* 72.8%

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

      3. distribute-lft-out 72.8%

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

      4. neg-mul-1 72.8%

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

   7. Simplified 72.8%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+42} \lor \neg \left(t \leq 2.5 \cdot 10^{+45}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{-a \cdot \left(z + b\right)}\\ \end{array} \]

Alternative 7: 57.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -550:\\ \;\;\;\;x \cdot \left(\left(1 - y \cdot t\right) + \left(y \cdot y\right) \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -550.0)
   (* x (+ (- 1.0 (* y t)) (* (* y y) (* 0.5 (* t t)))))
   (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -550.0) {
		tmp = x * ((1.0 - (y * t)) + ((y * y) * (0.5 * (t * 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 <= (-550.0d0)) then
        tmp = x * ((1.0d0 - (y * t)) + ((y * y) * (0.5d0 * (t * 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 <= -550.0) {
		tmp = x * ((1.0 - (y * t)) + ((y * y) * (0.5 * (t * t))));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -550.0:
		tmp = x * ((1.0 - (y * t)) + ((y * y) * (0.5 * (t * t))))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -550.0)
		tmp = Float64(x * Float64(Float64(1.0 - Float64(y * t)) + Float64(Float64(y * y) * Float64(0.5 * Float64(t * 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 <= -550.0)
		tmp = x * ((1.0 - (y * t)) + ((y * y) * (0.5 * (t * t))));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -550.0], N[(x * N[(N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision] + N[(N[(y * y), $MachinePrecision] * N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -550

   1. Initial program 94.9%

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

   2. Taylor expanded in t around inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. distribute-rgt-neg-in 78.6%

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

   4. Simplified 78.6%

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

   5. Taylor expanded in t around 0 49.2%

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-1 \cdot \left(t \cdot y\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 49.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -1 \cdot \left(t \cdot y\right)\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)} \]

      2. mul-1-neg 49.2%

         \[\leadsto x \cdot \left(\left(1 + \color{blue}{\left(-t \cdot y\right)}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      3. unsub-neg 49.2%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - t \cdot y\right)} + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      4. *-commutative 49.2%

         \[\leadsto x \cdot \left(\left(1 - \color{blue}{y \cdot t}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      5. associate-*r* 49.2%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + \color{blue}{\left(0.5 \cdot {t}^{2}\right) \cdot {y}^{2}}\right) \]

      6. unpow2 49.2%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + \left(0.5 \cdot \color{blue}{\left(t \cdot t\right)}\right) \cdot {y}^{2}\right) \]

      7. unpow2 49.2%

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

   7. Simplified 49.2%

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

   if -550 < t

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 65.8%

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

   3. Taylor expanded in t around 0 60.2%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -550:\\ \;\;\;\;x \cdot \left(\left(1 - y \cdot t\right) + \left(y \cdot y\right) \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 8: 41.8% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-100} \lor \neg \left(y \leq 2.4 \cdot 10^{-36}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot y\right)\right) \cdot \left(t \cdot \left(t \cdot 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(1 - a \cdot b\right) + 0.5 \cdot \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.1e-100) (not (<= y 2.4e-36)))
   (* (* x (* y y)) (* t (* t 0.5)))
   (* x (+ (- 1.0 (* a b)) (* 0.5 (* (* a b) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e-100) || !(y <= 2.4e-36)) {
		tmp = (x * (y * y)) * (t * (t * 0.5));
	} else {
		tmp = x * ((1.0 - (a * b)) + (0.5 * ((a * b) * (a * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.1d-100)) .or. (.not. (y <= 2.4d-36))) then
        tmp = (x * (y * y)) * (t * (t * 0.5d0))
    else
        tmp = x * ((1.0d0 - (a * b)) + (0.5d0 * ((a * b) * (a * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e-100) || !(y <= 2.4e-36)) {
		tmp = (x * (y * y)) * (t * (t * 0.5));
	} else {
		tmp = x * ((1.0 - (a * b)) + (0.5 * ((a * b) * (a * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.1e-100) or not (y <= 2.4e-36):
		tmp = (x * (y * y)) * (t * (t * 0.5))
	else:
		tmp = x * ((1.0 - (a * b)) + (0.5 * ((a * b) * (a * b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.1e-100) || !(y <= 2.4e-36))
		tmp = Float64(Float64(x * Float64(y * y)) * Float64(t * Float64(t * 0.5)));
	else
		tmp = Float64(x * Float64(Float64(1.0 - Float64(a * b)) + Float64(0.5 * Float64(Float64(a * b) * Float64(a * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.1e-100) || ~((y <= 2.4e-36)))
		tmp = (x * (y * y)) * (t * (t * 0.5));
	else
		tmp = x * ((1.0 - (a * b)) + (0.5 * ((a * b) * (a * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.1e-100], N[Not[LessEqual[y, 2.4e-36]], $MachinePrecision]], N[(N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision] * N[(t * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(a * b), $MachinePrecision] * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.09999999999999995e-100 or 2.4e-36 < y

   1. Initial program 96.3%

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

   2. Taylor expanded in t around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. distribute-rgt-neg-in 58.9%

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

   4. Simplified 58.9%

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

   5. Taylor expanded in t around 0 34.7%

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-1 \cdot \left(t \cdot y\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 34.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -1 \cdot \left(t \cdot y\right)\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)} \]

      2. mul-1-neg 34.7%

         \[\leadsto x \cdot \left(\left(1 + \color{blue}{\left(-t \cdot y\right)}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      3. unsub-neg 34.7%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - t \cdot y\right)} + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      4. *-commutative 34.7%

         \[\leadsto x \cdot \left(\left(1 - \color{blue}{y \cdot t}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      5. associate-*r* 34.7%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + \color{blue}{\left(0.5 \cdot {t}^{2}\right) \cdot {y}^{2}}\right) \]

      6. unpow2 34.7%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + \left(0.5 \cdot \color{blue}{\left(t \cdot t\right)}\right) \cdot {y}^{2}\right) \]

      7. unpow2 34.7%

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

   7. Simplified 34.7%

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

   8. Taylor expanded in y around inf 39.5%

      \[\leadsto \color{blue}{0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. unpow2 39.5%

         \[\leadsto 0.5 \cdot \left(\color{blue}{\left(t \cdot t\right)} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      2. associate-*r* 39.5%

         \[\leadsto \color{blue}{\left(0.5 \cdot \left(t \cdot t\right)\right) \cdot \left(x \cdot {y}^{2}\right)} \]

      3. *-commutative 39.5%

         \[\leadsto \color{blue}{\left(x \cdot {y}^{2}\right) \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)} \]

      4. unpow2 39.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot y\right)}\right) \cdot \left(0.5 \cdot \left(t \cdot t\right)\right) \]

      5. associate-*r* 39.5%

         \[\leadsto \left(x \cdot \left(y \cdot y\right)\right) \cdot \color{blue}{\left(\left(0.5 \cdot t\right) \cdot t\right)} \]

      6. *-commutative 39.5%

         \[\leadsto \left(x \cdot \left(y \cdot y\right)\right) \cdot \color{blue}{\left(t \cdot \left(0.5 \cdot t\right)\right)} \]

   10. Simplified 39.5%

       \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot y\right)\right) \cdot \left(t \cdot \left(0.5 \cdot t\right)\right)} \]

   if -1.09999999999999995e-100 < y < 2.4e-36

   1. Initial program 94.0%

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

   2. Taylor expanded in b around inf 84.0%

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

      1. associate-*r* 84.0%

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

      2. *-commutative 84.0%

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

      3. neg-mul-1 84.0%

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

   4. Simplified 84.0%

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

   5. Taylor expanded in b around 0 50.3%

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

      1. associate-+r+ 50.3%

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

      2. mul-1-neg 50.3%

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

      3. unsub-neg 50.3%

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

      4. unpow2 50.3%

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

      5. unpow2 50.3%

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

      6. unswap-sqr 52.3%

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

   7. Simplified 52.3%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-100} \lor \neg \left(y \leq 2.4 \cdot 10^{-36}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot y\right)\right) \cdot \left(t \cdot \left(t \cdot 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(1 - a \cdot b\right) + 0.5 \cdot \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 9: 39.2% accurate, 20.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-112} \lor \neg \left(y \leq 1.5 \cdot 10^{-36}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot y\right)\right) \cdot \left(t \cdot \left(t \cdot 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e-112) (not (<= y 1.5e-36)))
   (* (* x (* y y)) (* t (* t 0.5)))
   (* x (- 1.0 (* a (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e-112) || !(y <= 1.5e-36)) {
		tmp = (x * (y * y)) * (t * (t * 0.5));
	} else {
		tmp = x * (1.0 - (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 <= (-2.7d-112)) .or. (.not. (y <= 1.5d-36))) then
        tmp = (x * (y * y)) * (t * (t * 0.5d0))
    else
        tmp = x * (1.0d0 - (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 <= -2.7e-112) || !(y <= 1.5e-36)) {
		tmp = (x * (y * y)) * (t * (t * 0.5));
	} else {
		tmp = x * (1.0 - (a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.7e-112) or not (y <= 1.5e-36):
		tmp = (x * (y * y)) * (t * (t * 0.5))
	else:
		tmp = x * (1.0 - (a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.7e-112) || !(y <= 1.5e-36))
		tmp = Float64(Float64(x * Float64(y * y)) * Float64(t * Float64(t * 0.5)));
	else
		tmp = Float64(x * Float64(1.0 - 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 <= -2.7e-112) || ~((y <= 1.5e-36)))
		tmp = (x * (y * y)) * (t * (t * 0.5));
	else
		tmp = x * (1.0 - (a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.7e-112], N[Not[LessEqual[y, 1.5e-36]], $MachinePrecision]], N[(N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision] * N[(t * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000001e-112 or 1.5000000000000001e-36 < y

   1. Initial program 96.3%

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

   2. Taylor expanded in t around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. distribute-rgt-neg-in 58.9%

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

   4. Simplified 58.9%

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

   5. Taylor expanded in t around 0 34.7%

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-1 \cdot \left(t \cdot y\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 34.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -1 \cdot \left(t \cdot y\right)\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)} \]

      2. mul-1-neg 34.7%

         \[\leadsto x \cdot \left(\left(1 + \color{blue}{\left(-t \cdot y\right)}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      3. unsub-neg 34.7%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - t \cdot y\right)} + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      4. *-commutative 34.7%

         \[\leadsto x \cdot \left(\left(1 - \color{blue}{y \cdot t}\right) + 0.5 \cdot \left({t}^{2} \cdot {y}^{2}\right)\right) \]

      5. associate-*r* 34.7%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + \color{blue}{\left(0.5 \cdot {t}^{2}\right) \cdot {y}^{2}}\right) \]

      6. unpow2 34.7%

         \[\leadsto x \cdot \left(\left(1 - y \cdot t\right) + \left(0.5 \cdot \color{blue}{\left(t \cdot t\right)}\right) \cdot {y}^{2}\right) \]

      7. unpow2 34.7%

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

   7. Simplified 34.7%

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

   8. Taylor expanded in y around inf 39.5%

      \[\leadsto \color{blue}{0.5 \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. unpow2 39.5%

         \[\leadsto 0.5 \cdot \left(\color{blue}{\left(t \cdot t\right)} \cdot \left(x \cdot {y}^{2}\right)\right) \]

      2. associate-*r* 39.5%

         \[\leadsto \color{blue}{\left(0.5 \cdot \left(t \cdot t\right)\right) \cdot \left(x \cdot {y}^{2}\right)} \]

      3. *-commutative 39.5%

         \[\leadsto \color{blue}{\left(x \cdot {y}^{2}\right) \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)} \]

      4. unpow2 39.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot y\right)}\right) \cdot \left(0.5 \cdot \left(t \cdot t\right)\right) \]

      5. associate-*r* 39.5%

         \[\leadsto \left(x \cdot \left(y \cdot y\right)\right) \cdot \color{blue}{\left(\left(0.5 \cdot t\right) \cdot t\right)} \]

      6. *-commutative 39.5%

         \[\leadsto \left(x \cdot \left(y \cdot y\right)\right) \cdot \color{blue}{\left(t \cdot \left(0.5 \cdot t\right)\right)} \]

   10. Simplified 39.5%

       \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot y\right)\right) \cdot \left(t \cdot \left(0.5 \cdot t\right)\right)} \]

   if -2.7000000000000001e-112 < y < 1.5000000000000001e-36

   1. Initial program 94.0%

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

   2. Taylor expanded in y around 0 84.0%

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

      1. sub-neg 84.0%

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

      2. neg-mul-1 84.0%

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

      3. log1p-def 90.0%

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

      4. neg-mul-1 90.0%

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

      5. sub-neg 90.0%

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

      6. sub-neg 90.0%

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

   4. Simplified 90.0%

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

   5. Taylor expanded in z around 0 90.0%

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

      1. associate-*r* 90.0%

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

      2. associate-*r* 90.0%

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

      3. distribute-lft-out 90.0%

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

      4. neg-mul-1 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in a around 0 49.2%

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

      1. neg-mul-1 49.2%

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

      2. unsub-neg 49.2%

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

   10. Simplified 49.2%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-112} \lor \neg \left(y \leq 1.5 \cdot 10^{-36}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot y\right)\right) \cdot \left(t \cdot \left(t \cdot 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \end{array} \]

Alternative 10: 32.8% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+72} \lor \neg \left(t \leq 11000000000000\right):\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.65e+72) (not (<= t 11000000000000.0)))
   (* x (- 1.0 (* y t)))
   (* x (- 1.0 (* a (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.65e+72) || !(t <= 11000000000000.0)) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * (1.0 - (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 ((t <= (-1.65d+72)) .or. (.not. (t <= 11000000000000.0d0))) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = x * (1.0d0 - (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 ((t <= -1.65e+72) || !(t <= 11000000000000.0)) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * (1.0 - (a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.65e+72) or not (t <= 11000000000000.0):
		tmp = x * (1.0 - (y * t))
	else:
		tmp = x * (1.0 - (a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.65e+72) || !(t <= 11000000000000.0))
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(a * Float64(z + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.65e+72) || ~((t <= 11000000000000.0)))
		tmp = x * (1.0 - (y * t));
	else
		tmp = x * (1.0 - (a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.65e+72], N[Not[LessEqual[t, 11000000000000.0]], $MachinePrecision]], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65e72 or 1.1e13 < t

   1. Initial program 94.9%

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

   2. Taylor expanded in t around inf 81.1%

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

      1. mul-1-neg 81.1%

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

      2. distribute-rgt-neg-in 81.1%

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

   4. Simplified 81.1%

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

   5. Taylor expanded in t around 0 38.0%

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

      1. mul-1-neg 38.0%

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

      2. unsub-neg 38.0%

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

      3. *-commutative 38.0%

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

   7. Simplified 38.0%

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

   if -1.65e72 < t < 1.1e13

   1. Initial program 95.9%

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

   2. Taylor expanded in y around 0 66.6%

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

      1. sub-neg 66.6%

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

      2. neg-mul-1 66.6%

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

      3. log1p-def 71.9%

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

      4. neg-mul-1 71.9%

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

      5. sub-neg 71.9%

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

      6. sub-neg 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in z around 0 71.9%

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

      1. associate-*r* 71.9%

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

      2. associate-*r* 71.9%

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

      3. distribute-lft-out 71.9%

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

      4. neg-mul-1 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in a around 0 35.0%

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

      1. neg-mul-1 35.0%

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

      2. unsub-neg 35.0%

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

   10. Simplified 35.0%

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

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+72} \lor \neg \left(t \leq 11000000000000\right):\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \end{array} \]

Alternative 11: 22.9% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-106} \lor \neg \left(b \leq 1.75 \cdot 10^{-19}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.8e+114)
   (* a (* x (- b)))
   (if (or (<= b -6.2e-106) (not (<= b 1.75e-19))) (* a (* x (- z))) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+114) {
		tmp = a * (x * -b);
	} else if ((b <= -6.2e-106) || !(b <= 1.75e-19)) {
		tmp = a * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.8d+114)) then
        tmp = a * (x * -b)
    else if ((b <= (-6.2d-106)) .or. (.not. (b <= 1.75d-19))) then
        tmp = a * (x * -z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+114) {
		tmp = a * (x * -b);
	} else if ((b <= -6.2e-106) || !(b <= 1.75e-19)) {
		tmp = a * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.8e+114:
		tmp = a * (x * -b)
	elif (b <= -6.2e-106) or not (b <= 1.75e-19):
		tmp = a * (x * -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.8e+114)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif ((b <= -6.2e-106) || !(b <= 1.75e-19))
		tmp = Float64(a * Float64(x * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.8e+114)
		tmp = a * (x * -b);
	elseif ((b <= -6.2e-106) || ~((b <= 1.75e-19)))
		tmp = a * (x * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.8e+114], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -6.2e-106], N[Not[LessEqual[b, 1.75e-19]], $MachinePrecision]], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if b < -6.8000000000000001e114

   1. Initial program 97.3%

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

   2. Taylor expanded in b around inf 79.2%

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

      1. associate-*r* 79.2%

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

      2. *-commutative 79.2%

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

      3. neg-mul-1 79.2%

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

   4. Simplified 79.2%

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

   5. Taylor expanded in b around 0 34.5%

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

      1. mul-1-neg 34.5%

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

      2. unsub-neg 34.5%

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

   7. Simplified 34.5%

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

   8. Taylor expanded in a around inf 29.0%

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

      1. mul-1-neg 29.0%

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

      2. distribute-rgt-neg-in 29.0%

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

   10. Simplified 29.0%

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

   if -6.8000000000000001e114 < b < -6.19999999999999971e-106 or 1.75000000000000008e-19 < b

   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. Taylor expanded in y around 0 61.0%

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

      1. sub-neg 61.0%

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

      2. neg-mul-1 61.0%

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

      3. log1p-def 61.0%

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

      4. neg-mul-1 61.0%

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

      5. sub-neg 61.0%

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

      6. sub-neg 61.0%

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

   4. Simplified 61.0%

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

   5. Taylor expanded in z around 0 61.0%

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

      1. associate-*r* 61.0%

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

      2. associate-*r* 61.0%

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

      3. distribute-lft-out 61.0%

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

      4. neg-mul-1 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in a around 0 16.1%

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

      1. mul-1-neg 16.1%

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

      2. unsub-neg 16.1%

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

      3. *-commutative 16.1%

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

   10. Simplified 16.1%

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

   11. Taylor expanded in z around inf 26.6%

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

       1. associate-*r* 26.6%

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

       2. neg-mul-1 26.6%

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

   13. Simplified 26.6%

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

   if -6.19999999999999971e-106 < b < 1.75000000000000008e-19

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf 81.1%

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

   3. Taylor expanded in y around 0 26.2%

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

4. Final simplification 26.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-106} \lor \neg \left(b \leq 1.75 \cdot 10^{-19}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 30.2% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-42} \lor \neg \left(x \leq 9.8 \cdot 10^{-80}\right):\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.55e-42) (not (<= x 9.8e-80)))
   (* x (- 1.0 (* a b)))
   (* a (* x (- z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.55e-42) || !(x <= 9.8e-80)) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.55d-42)) .or. (.not. (x <= 9.8d-80))) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.55e-42) || !(x <= 9.8e-80)) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.55e-42) or not (x <= 9.8e-80):
		tmp = x * (1.0 - (a * b))
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.55e-42) || !(x <= 9.8e-80))
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.55e-42) || ~((x <= 9.8e-80)))
		tmp = x * (1.0 - (a * b));
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.55e-42], N[Not[LessEqual[x, 9.8e-80]], $MachinePrecision]], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5500000000000001e-42 or 9.79999999999999981e-80 < x

   1. Initial program 95.4%

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

   2. Taylor expanded in b around inf 54.1%

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

      1. associate-*r* 54.1%

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

      2. *-commutative 54.1%

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

      3. neg-mul-1 54.1%

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

   4. Simplified 54.1%

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

   5. Taylor expanded in b around 0 27.8%

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

      1. mul-1-neg 27.8%

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

      2. unsub-neg 27.8%

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

   7. Simplified 27.8%

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

   if -1.5500000000000001e-42 < x < 9.79999999999999981e-80

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0 58.1%

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

      1. sub-neg 58.1%

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

      2. neg-mul-1 58.1%

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

      3. log1p-def 63.4%

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

      4. neg-mul-1 63.4%

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

      5. sub-neg 63.4%

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

      6. sub-neg 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in z around 0 63.4%

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

      1. associate-*r* 63.4%

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

      2. associate-*r* 63.4%

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

      3. distribute-lft-out 63.4%

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

      4. neg-mul-1 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in a around 0 15.4%

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

      1. mul-1-neg 15.4%

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

      2. unsub-neg 15.4%

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

      3. *-commutative 15.4%

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

   10. Simplified 15.4%

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

   11. Taylor expanded in z around inf 33.8%

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

       1. associate-*r* 33.8%

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

       2. neg-mul-1 33.8%

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

   13. Simplified 33.8%

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

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-42} \lor \neg \left(x \leq 9.8 \cdot 10^{-80}\right):\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 13: 32.4% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+72} \lor \neg \left(t \leq 1250000000000\right):\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.3e+72) (not (<= t 1250000000000.0)))
   (* x (- 1.0 (* y t)))
   (* x (- 1.0 (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.3e+72) || !(t <= 1250000000000.0)) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.3d+72)) .or. (.not. (t <= 1250000000000.0d0))) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = x * (1.0d0 - (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.3e+72) || !(t <= 1250000000000.0)) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.3e+72) or not (t <= 1250000000000.0):
		tmp = x * (1.0 - (y * t))
	else:
		tmp = x * (1.0 - (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.3e+72) || !(t <= 1250000000000.0))
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.3e+72) || ~((t <= 1250000000000.0)))
		tmp = x * (1.0 - (y * t));
	else
		tmp = x * (1.0 - (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.3e+72], N[Not[LessEqual[t, 1250000000000.0]], $MachinePrecision]], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999991e72 or 1.25e12 < t

   1. Initial program 94.9%

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

   2. Taylor expanded in t around inf 81.1%

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

      1. mul-1-neg 81.1%

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

      2. distribute-rgt-neg-in 81.1%

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

   4. Simplified 81.1%

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

   5. Taylor expanded in t around 0 38.0%

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

      1. mul-1-neg 38.0%

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

      2. unsub-neg 38.0%

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

      3. *-commutative 38.0%

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

   7. Simplified 38.0%

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

   if -1.29999999999999991e72 < t < 1.25e12

   1. Initial program 95.9%

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

   2. Taylor expanded in b around inf 65.8%

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

      1. associate-*r* 65.8%

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

      2. *-commutative 65.8%

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

      3. neg-mul-1 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in b around 0 33.7%

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

      1. mul-1-neg 33.7%

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

      2. unsub-neg 33.7%

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

   7. Simplified 33.7%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+72} \lor \neg \left(t \leq 1250000000000\right):\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \]

Alternative 14: 31.7% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+68} \lor \neg \left(t \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.5e+68) (not (<= t 5.1e-8)))
   (* x (- 1.0 (* y t)))
   (- x (* b (* x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.5e+68) || !(t <= 5.1e-8)) {
		tmp = x * (1.0 - (y * t));
	} 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 ((t <= (-2.5d+68)) .or. (.not. (t <= 5.1d-8))) then
        tmp = x * (1.0d0 - (y * t))
    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 ((t <= -2.5e+68) || !(t <= 5.1e-8)) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x - (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.5e+68) or not (t <= 5.1e-8):
		tmp = x * (1.0 - (y * t))
	else:
		tmp = x - (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.5e+68) || !(t <= 5.1e-8))
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	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 ((t <= -2.5e+68) || ~((t <= 5.1e-8)))
		tmp = x * (1.0 - (y * t));
	else
		tmp = x - (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.5e+68], N[Not[LessEqual[t, 5.1e-8]], $MachinePrecision]], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5000000000000002e68 or 5.10000000000000001e-8 < t

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf 80.7%

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

      1. mul-1-neg 80.7%

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

      2. distribute-rgt-neg-in 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in t around 0 38.7%

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

      1. mul-1-neg 38.7%

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

      2. unsub-neg 38.7%

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

      3. *-commutative 38.7%

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

   7. Simplified 38.7%

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

   if -2.5000000000000002e68 < t < 5.10000000000000001e-8

   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. Taylor expanded in y around 0 65.8%

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

      1. sub-neg 65.8%

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

      2. neg-mul-1 65.8%

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

      3. log1p-def 71.3%

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

      4. neg-mul-1 71.3%

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

      5. sub-neg 71.3%

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

      6. sub-neg 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in z around 0 71.3%

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

      1. associate-*r* 71.3%

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

      2. associate-*r* 71.3%

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

      3. distribute-lft-out 71.3%

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

      4. neg-mul-1 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in a around 0 31.6%

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

      1. mul-1-neg 31.6%

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

      2. unsub-neg 31.6%

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

      3. *-commutative 31.6%

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

   10. Simplified 31.6%

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

   11. Taylor expanded in b around inf 30.4%

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

       1. *-commutative 30.4%

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

       2. associate-*r* 33.0%

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

   13. Simplified 33.0%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+68} \lor \neg \left(t \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 15: 26.7% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-82} \lor \neg \left(y \leq 1.06 \cdot 10^{-70}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.3e-82) (not (<= y 1.06e-70))) (* a (* x (- b))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e-82) || !(y <= 1.06e-70)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.3d-82)) .or. (.not. (y <= 1.06d-70))) then
        tmp = a * (x * -b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e-82) || !(y <= 1.06e-70)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.3e-82) or not (y <= 1.06e-70):
		tmp = a * (x * -b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.3e-82) || !(y <= 1.06e-70))
		tmp = Float64(a * Float64(x * Float64(-b)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.3e-82) || ~((y <= 1.06e-70)))
		tmp = a * (x * -b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.3e-82], N[Not[LessEqual[y, 1.06e-70]], $MachinePrecision]], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.30000000000000022e-82 or 1.06e-70 < y

   1. Initial program 95.7%

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

   2. Taylor expanded in b around inf 38.4%

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

      1. associate-*r* 38.4%

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

      2. *-commutative 38.4%

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

      3. neg-mul-1 38.4%

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

   4. Simplified 38.4%

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

   5. Taylor expanded in b around 0 13.3%

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

      1. mul-1-neg 13.3%

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

      2. unsub-neg 13.3%

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

   7. Simplified 13.3%

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

   8. Taylor expanded in a around inf 17.1%

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

      1. mul-1-neg 17.1%

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

      2. distribute-rgt-neg-in 17.1%

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

   10. Simplified 17.1%

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

   if -3.30000000000000022e-82 < y < 1.06e-70

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 48.2%

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

   3. Taylor expanded in y around 0 35.0%

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

4. Final simplification 23.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-82} \lor \neg \left(y \leq 1.06 \cdot 10^{-70}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 26.6% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.1e-83)
   (* a (* x (- z)))
   (if (<= y 1.35e-70) x (* b (* x (- a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.1e-83) {
		tmp = a * (x * -z);
	} else if (y <= 1.35e-70) {
		tmp = x;
	} else {
		tmp = b * (x * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.1d-83)) then
        tmp = a * (x * -z)
    else if (y <= 1.35d-70) then
        tmp = x
    else
        tmp = b * (x * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.1e-83) {
		tmp = a * (x * -z);
	} else if (y <= 1.35e-70) {
		tmp = x;
	} else {
		tmp = b * (x * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.1e-83:
		tmp = a * (x * -z)
	elif y <= 1.35e-70:
		tmp = x
	else:
		tmp = b * (x * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.1e-83)
		tmp = Float64(a * Float64(x * Float64(-z)));
	elseif (y <= 1.35e-70)
		tmp = x;
	else
		tmp = Float64(b * Float64(x * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.1e-83)
		tmp = a * (x * -z);
	elseif (y <= 1.35e-70)
		tmp = x;
	else
		tmp = b * (x * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.1e-83], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-70], x, N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.09999999999999992e-83

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 44.6%

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

      1. sub-neg 44.6%

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

      2. neg-mul-1 44.6%

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

      3. log1p-def 46.9%

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

      4. neg-mul-1 46.9%

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

      5. sub-neg 46.9%

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

      6. sub-neg 46.9%

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

   4. Simplified 46.9%

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

   5. Taylor expanded in z around 0 46.9%

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

      1. associate-*r* 46.9%

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

      2. associate-*r* 46.9%

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

      3. distribute-lft-out 46.9%

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

      4. neg-mul-1 46.9%

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

   7. Simplified 46.9%

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

   8. Taylor expanded in a around 0 12.1%

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

      1. mul-1-neg 12.1%

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

      2. unsub-neg 12.1%

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

      3. *-commutative 12.1%

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

   10. Simplified 12.1%

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

   11. Taylor expanded in z around inf 18.0%

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

       1. associate-*r* 18.0%

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

       2. neg-mul-1 18.0%

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

   13. Simplified 18.0%

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

   if -3.09999999999999992e-83 < y < 1.3500000000000001e-70

   1. Initial program 94.8%

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

   2. Taylor expanded in y around inf 48.1%

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

   3. Taylor expanded in y around 0 35.7%

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

   if 1.3500000000000001e-70 < y

   1. Initial program 94.2%

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

   2. Taylor expanded in b around inf 33.9%

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

      1. associate-*r* 33.9%

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

      2. *-commutative 33.9%

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

      3. neg-mul-1 33.9%

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

   4. Simplified 33.9%

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

   5. Taylor expanded in b around 0 13.5%

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

      1. mul-1-neg 13.5%

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

      2. unsub-neg 13.5%

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

   7. Simplified 13.5%

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

   8. Taylor expanded in a around inf 19.0%

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

      1. mul-1-neg 19.0%

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

      2. distribute-rgt-neg-in 19.0%

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

   10. Simplified 19.0%

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

   11. Taylor expanded in a around 0 19.0%

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

       1. associate-*r* 19.0%

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

       2. neg-mul-1 19.0%

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

       3. *-commutative 19.0%

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

       4. associate-*r* 24.6%

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

   13. Simplified 24.6%

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

4. Final simplification 26.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 17: 18.8% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-98}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b -1e-98) (* t (* x y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e-98) {
		tmp = t * (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1d-98)) then
        tmp = t * (x * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e-98) {
		tmp = t * (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1e-98:
		tmp = t * (x * y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1e-98)
		tmp = Float64(t * Float64(x * y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1e-98)
		tmp = t * (x * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1e-98], N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -9.99999999999999939e-99

   1. Initial program 98.6%

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

   2. Taylor expanded in t around inf 48.4%

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

      1. mul-1-neg 48.4%

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

      2. distribute-rgt-neg-in 48.4%

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

   4. Simplified 48.4%

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

      1. expm1-log1p-u 48.4%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{t \cdot \left(-y\right)}\right)\right)} \]

      2. expm1-udef 48.4%

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

      3. exp-prod 51.8%

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

      4. add-sqr-sqrt 26.1%

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

      5. sqrt-unprod 29.5%

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

      6. sqr-neg 29.5%

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

      7. sqrt-unprod 9.4%

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

      8. add-sqr-sqrt 16.0%

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

   6. Applied egg-rr 16.0%

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

      1. expm1-def 16.0%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{t}\right)}^{y}\right)\right)} \]

      2. expm1-log1p 16.0%

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

      3. exp-prod 23.2%

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

      4. *-commutative 23.2%

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

   8. Simplified 23.2%

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

   9. Taylor expanded in y around 0 16.0%

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

   10. Taylor expanded in t around inf 20.2%

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

   if -9.99999999999999939e-99 < b

   1. Initial program 93.9%

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

   2. Taylor expanded in y around inf 71.9%

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

   3. Taylor expanded in y around 0 18.5%

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

4. Final simplification 19.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-98}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 19.5% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.4%

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

2. Taylor expanded in y around inf 69.7%

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

3. Taylor expanded in y around 0 16.6%

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

4. Final simplification 16.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023290 
(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))))))