Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A

Percentage Accurate: 99.8% → 99.8%

Time: 13.7s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x + (y + (z + (((-0.5d0) * b) + (b * a))))) - (z * log(t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

2. Taylor expanded in a around 0 99.9%

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

3. Final simplification 99.9%

   \[\leadsto \left(x + \left(y + \left(z + \left(-0.5 \cdot b + b \cdot a\right)\right)\right)\right) - z \cdot \log t \]

Alternative 2: 91.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+47} \lor \neg \left(t_1 \leq 2 \cdot 10^{+52}\right):\\ \;\;\;\;\left(x + y\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y + \left(z + -0.5 \cdot b\right)\right)\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -5e+47) (not (<= t_1 2e+52)))
     (+ (+ x y) t_1)
     (- (+ x (+ y (+ z (* -0.5 b)))) (* z (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -5e+47) || !(t_1 <= 2e+52)) {
		tmp = (x + y) + t_1;
	} else {
		tmp = (x + (y + (z + (-0.5 * b)))) - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-5d+47)) .or. (.not. (t_1 <= 2d+52))) then
        tmp = (x + y) + t_1
    else
        tmp = (x + (y + (z + ((-0.5d0) * b)))) - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -5e+47) || !(t_1 <= 2e+52)) {
		tmp = (x + y) + t_1;
	} else {
		tmp = (x + (y + (z + (-0.5 * b)))) - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -5e+47) or not (t_1 <= 2e+52):
		tmp = (x + y) + t_1
	else:
		tmp = (x + (y + (z + (-0.5 * b)))) - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -5e+47) || !(t_1 <= 2e+52))
		tmp = Float64(Float64(x + y) + t_1);
	else
		tmp = Float64(Float64(x + Float64(y + Float64(z + Float64(-0.5 * b)))) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -5e+47) || ~((t_1 <= 2e+52)))
		tmp = (x + y) + t_1;
	else
		tmp = (x + (y + (z + (-0.5 * b)))) - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+47], N[Not[LessEqual[t$95$1, 2e+52]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(x + N[(y + N[(z + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -5.00000000000000022e47 or 2e52 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 91.2%

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

      1. +-commutative 91.2%

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

   4. Simplified 91.2%

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

   if -5.00000000000000022e47 < (*.f64 (-.f64 a 1/2) b) < 2e52

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 95.0%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+47} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+52}\right):\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y + \left(z + -0.5 \cdot b\right)\right)\right) - z \cdot \log t\\ \end{array} \]

Alternative 3: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -1 \cdot 10^{+173}:\\ \;\;\;\;\left(x + y\right) + t_1\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{+17}:\\ \;\;\;\;t_1 + \left(z - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= (+ x y) -1e+173)
     (+ (+ x y) t_1)
     (if (<= (+ x y) 2e+17) (+ t_1 (- z (* z (log t)))) (+ y t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -1e+173) {
		tmp = (x + y) + t_1;
	} else if ((x + y) <= 2e+17) {
		tmp = t_1 + (z - (z * log(t)));
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= (-1d+173)) then
        tmp = (x + y) + t_1
    else if ((x + y) <= 2d+17) then
        tmp = t_1 + (z - (z * log(t)))
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -1e+173) {
		tmp = (x + y) + t_1;
	} else if ((x + y) <= 2e+17) {
		tmp = t_1 + (z - (z * Math.log(t)));
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -1e+173:
		tmp = (x + y) + t_1
	elif (x + y) <= 2e+17:
		tmp = t_1 + (z - (z * math.log(t)))
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= -1e+173)
		tmp = Float64(Float64(x + y) + t_1);
	elseif (Float64(x + y) <= 2e+17)
		tmp = Float64(t_1 + Float64(z - Float64(z * log(t))));
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= -1e+173)
		tmp = (x + y) + t_1;
	elseif ((x + y) <= 2e+17)
		tmp = t_1 + (z - (z * log(t)));
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -1e+173], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 2e+17], N[(t$95$1 + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1e173

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 97.0%

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

      1. +-commutative 97.0%

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

   4. Simplified 97.0%

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

   if -1e173 < (+.f64 x y) < 2e17

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around inf 88.7%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right)} + \left(a - 0.5\right) \cdot b \]
   3. Step-by-step derivation

      1. sub-neg 88.7%

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

      2. distribute-rgt-in 88.8%

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

      3. *-lft-identity 88.8%

         \[\leadsto \left(\color{blue}{z} + \left(-\log t\right) \cdot z\right) + \left(a - 0.5\right) \cdot b \]

      4. cancel-sign-sub-inv 88.8%

         \[\leadsto \color{blue}{\left(z - \log t \cdot z\right)} + \left(a - 0.5\right) \cdot b \]

      5. *-commutative 88.8%

         \[\leadsto \left(z - \color{blue}{z \cdot \log t}\right) + \left(a - 0.5\right) \cdot b \]

   4. Simplified 88.8%

      \[\leadsto \color{blue}{\left(z - z \cdot \log t\right)} + \left(a - 0.5\right) \cdot b \]

   if 2e17 < (+.f64 x y)

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in y around inf 45.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+173}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = ((z + (x + y)) - (z * log(t))) + (b * (a - 0.5d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

2. Final simplification 99.9%

   \[\leadsto \left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + b \cdot \left(a - 0.5\right) \]

Alternative 5: 82.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+238} \lor \neg \left(z \leq 1.65 \cdot 10^{+181}\right) \land \left(z \leq 3.3 \cdot 10^{+224} \lor \neg \left(z \leq 3.4 \cdot 10^{+264}\right)\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.8e+238)
         (and (not (<= z 1.65e+181))
              (or (<= z 3.3e+224) (not (<= z 3.4e+264)))))
   (* z (- 1.0 (log t)))
   (+ (+ x y) (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.8e+238) || (!(z <= 1.65e+181) && ((z <= 3.3e+224) || !(z <= 3.4e+264)))) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = (x + y) + (b * (a - 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) :: tmp
    if ((z <= (-4.8d+238)) .or. (.not. (z <= 1.65d+181)) .and. (z <= 3.3d+224) .or. (.not. (z <= 3.4d+264))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = (x + y) + (b * (a - 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 tmp;
	if ((z <= -4.8e+238) || (!(z <= 1.65e+181) && ((z <= 3.3e+224) || !(z <= 3.4e+264)))) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = (x + y) + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.8e+238) or (not (z <= 1.65e+181) and ((z <= 3.3e+224) or not (z <= 3.4e+264))):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = (x + y) + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.8e+238) || (!(z <= 1.65e+181) && ((z <= 3.3e+224) || !(z <= 3.4e+264))))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.8e+238) || (~((z <= 1.65e+181)) && ((z <= 3.3e+224) || ~((z <= 3.4e+264)))))
		tmp = z * (1.0 - log(t));
	else
		tmp = (x + y) + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.8e+238], And[N[Not[LessEqual[z, 1.65e+181]], $MachinePrecision], Or[LessEqual[z, 3.3e+224], N[Not[LessEqual[z, 3.4e+264]], $MachinePrecision]]]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e238 or 1.65000000000000008e181 < z < 3.29999999999999996e224 or 3.4000000000000001e264 < z

   1. Initial program 99.4%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.4%

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

   3. Taylor expanded in z around inf 78.7%

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

   if -4.8e238 < z < 1.65000000000000008e181 or 3.29999999999999996e224 < z < 3.4000000000000001e264

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 89.6%

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

      1. +-commutative 89.6%

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

   4. Simplified 89.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+238} \lor \neg \left(z \leq 1.65 \cdot 10^{+181}\right) \land \left(z \leq 3.3 \cdot 10^{+224} \lor \neg \left(z \leq 3.4 \cdot 10^{+264}\right)\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 6: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-89} \lor \neg \left(b \leq 2.85 \cdot 10^{-40}\right):\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y + z\right)\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.5e-89) (not (<= b 2.85e-40)))
   (+ (+ x y) (* b (- a 0.5)))
   (- (+ x (+ y z)) (* z (log t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e-89) || !(b <= 2.85e-40)) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = (x + (y + z)) - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-7.5d-89)) .or. (.not. (b <= 2.85d-40))) then
        tmp = (x + y) + (b * (a - 0.5d0))
    else
        tmp = (x + (y + z)) - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e-89) || !(b <= 2.85e-40)) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = (x + (y + z)) - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.5e-89) or not (b <= 2.85e-40):
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = (x + (y + z)) - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.5e-89) || !(b <= 2.85e-40))
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(Float64(x + Float64(y + z)) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.5e-89) || ~((b <= 2.85e-40)))
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = (x + (y + z)) - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.5e-89], N[Not[LessEqual[b, 2.85e-40]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.4999999999999999e-89 or 2.84999999999999992e-40 < b

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 89.2%

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

      1. +-commutative 89.2%

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

   4. Simplified 89.2%

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

   if -7.4999999999999999e-89 < b < 2.84999999999999992e-40

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.8%

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

   3. Taylor expanded in b around 0 90.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-89} \lor \neg \left(b \leq 2.85 \cdot 10^{-40}\right):\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y + z\right)\right) - z \cdot \log t\\ \end{array} \]

Alternative 7: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+238} \lor \neg \left(z \leq 1.05 \cdot 10^{+148}\right):\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.45e+238) (not (<= z 1.05e+148)))
   (+ x (* z (- 1.0 (log t))))
   (+ (+ x y) (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.45e+238) || !(z <= 1.05e+148)) {
		tmp = x + (z * (1.0 - log(t)));
	} else {
		tmp = (x + y) + (b * (a - 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) :: tmp
    if ((z <= (-1.45d+238)) .or. (.not. (z <= 1.05d+148))) then
        tmp = x + (z * (1.0d0 - log(t)))
    else
        tmp = (x + y) + (b * (a - 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 tmp;
	if ((z <= -1.45e+238) || !(z <= 1.05e+148)) {
		tmp = x + (z * (1.0 - Math.log(t)));
	} else {
		tmp = (x + y) + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.45e+238) or not (z <= 1.05e+148):
		tmp = x + (z * (1.0 - math.log(t)))
	else:
		tmp = (x + y) + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.45e+238) || !(z <= 1.05e+148))
		tmp = Float64(x + Float64(z * Float64(1.0 - log(t))));
	else
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.45e+238) || ~((z <= 1.05e+148)))
		tmp = x + (z * (1.0 - log(t)));
	else
		tmp = (x + y) + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.45e+238], N[Not[LessEqual[z, 1.05e+148]], $MachinePrecision]], N[(x + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4500000000000001e238 or 1.04999999999999999e148 < z

   1. Initial program 99.5%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.5%

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

   3. Taylor expanded in b around 0 83.9%

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

      1. sub-neg 83.9%

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

      2. associate-+r+ 83.9%

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

      3. associate-+r+ 83.9%

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

      4. *-rgt-identity 83.9%

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

      5. distribute-rgt-neg-in 83.9%

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

      6. distribute-lft-in 83.9%

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

      7. sub-neg 83.9%

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

      8. associate-+r+ 83.9%

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

      9. +-commutative 83.9%

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

      10. fma-def 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in y around 0 72.6%

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

   if -1.4500000000000001e238 < z < 1.04999999999999999e148

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 90.6%

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

      1. +-commutative 90.6%

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

   4. Simplified 90.6%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+238} \lor \neg \left(z \leq 1.05 \cdot 10^{+148}\right):\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 8: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+237}:\\ \;\;\;\;x + t_1\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+181}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -3.2e+237)
     (+ x t_1)
     (if (<= z 1.66e+181) (+ (+ x y) (* b (- a 0.5))) (+ y t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double tmp;
	if (z <= -3.2e+237) {
		tmp = x + t_1;
	} else if (z <= 1.66e+181) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    if (z <= (-3.2d+237)) then
        tmp = x + t_1
    else if (z <= 1.66d+181) then
        tmp = (x + y) + (b * (a - 0.5d0))
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -3.2e+237) {
		tmp = x + t_1;
	} else if (z <= 1.66e+181) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -3.2e+237:
		tmp = x + t_1
	elif z <= 1.66e+181:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -3.2e+237)
		tmp = Float64(x + t_1);
	elseif (z <= 1.66e+181)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -3.2e+237)
		tmp = x + t_1;
	elseif (z <= 1.66e+181)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+237], N[(x + t$95$1), $MachinePrecision], If[LessEqual[z, 1.66e+181], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.20000000000000017e237

   1. Initial program 99.3%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.3%

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

   3. Taylor expanded in b around 0 99.3%

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

      1. sub-neg 99.3%

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

      2. associate-+r+ 99.3%

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

      3. associate-+r+ 99.3%

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

      4. *-rgt-identity 99.3%

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

      5. distribute-rgt-neg-in 99.3%

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

      6. distribute-lft-in 99.4%

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

      7. sub-neg 99.4%

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

      8. associate-+r+ 99.4%

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

      9. +-commutative 99.4%

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

      10. fma-def 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in y around 0 94.1%

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

   if -3.20000000000000017e237 < z < 1.6600000000000002e181

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 90.4%

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

      1. +-commutative 90.4%

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

   4. Simplified 90.4%

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

   if 1.6600000000000002e181 < z

   1. Initial program 99.5%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.5%

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

   3. Taylor expanded in b around 0 79.9%

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

      1. sub-neg 79.9%

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

      2. associate-+r+ 79.9%

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

      3. associate-+r+ 79.9%

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

      4. *-rgt-identity 79.9%

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

      5. distribute-rgt-neg-in 79.9%

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

      6. distribute-lft-in 79.9%

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

      7. sub-neg 79.9%

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

      8. associate-+r+ 79.9%

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

      9. +-commutative 79.9%

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

      10. fma-def 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in x around 0 72.4%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+237}:\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+181}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \end{array} \]

Alternative 9: 49.9% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot a\\ \mathbf{if}\;x + y \leq -4 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x + y \leq -5 \cdot 10^{+40}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{elif}\;x + y \leq -2 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x + y \leq 10^{-16}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b a))))
   (if (<= (+ x y) -4e+114)
     t_1
     (if (<= (+ x y) -5e+40)
       (+ x (* -0.5 b))
       (if (<= (+ x y) -2e-48)
         t_1
         (if (<= (+ x y) 1e-16) (* b (- a 0.5)) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * a);
	double tmp;
	if ((x + y) <= -4e+114) {
		tmp = t_1;
	} else if ((x + y) <= -5e+40) {
		tmp = x + (-0.5 * b);
	} else if ((x + y) <= -2e-48) {
		tmp = t_1;
	} else if ((x + y) <= 1e-16) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * a)
    if ((x + y) <= (-4d+114)) then
        tmp = t_1
    else if ((x + y) <= (-5d+40)) then
        tmp = x + ((-0.5d0) * b)
    else if ((x + y) <= (-2d-48)) then
        tmp = t_1
    else if ((x + y) <= 1d-16) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * a);
	double tmp;
	if ((x + y) <= -4e+114) {
		tmp = t_1;
	} else if ((x + y) <= -5e+40) {
		tmp = x + (-0.5 * b);
	} else if ((x + y) <= -2e-48) {
		tmp = t_1;
	} else if ((x + y) <= 1e-16) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * a)
	tmp = 0
	if (x + y) <= -4e+114:
		tmp = t_1
	elif (x + y) <= -5e+40:
		tmp = x + (-0.5 * b)
	elif (x + y) <= -2e-48:
		tmp = t_1
	elif (x + y) <= 1e-16:
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * a))
	tmp = 0.0
	if (Float64(x + y) <= -4e+114)
		tmp = t_1;
	elseif (Float64(x + y) <= -5e+40)
		tmp = Float64(x + Float64(-0.5 * b));
	elseif (Float64(x + y) <= -2e-48)
		tmp = t_1;
	elseif (Float64(x + y) <= 1e-16)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * a);
	tmp = 0.0;
	if ((x + y) <= -4e+114)
		tmp = t_1;
	elseif ((x + y) <= -5e+40)
		tmp = x + (-0.5 * b);
	elseif ((x + y) <= -2e-48)
		tmp = t_1;
	elseif ((x + y) <= 1e-16)
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -4e+114], t$95$1, If[LessEqual[N[(x + y), $MachinePrecision], -5e+40], N[(x + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], -2e-48], t$95$1, If[LessEqual[N[(x + y), $MachinePrecision], 1e-16], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x y) < -4e114 or -5.00000000000000003e40 < (+.f64 x y) < -1.9999999999999999e-48

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in x around inf 54.0%

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

   3. Taylor expanded in a around inf 46.4%

      \[\leadsto x + \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative 46.4%

         \[\leadsto x + \color{blue}{b \cdot a} \]

   5. Simplified 46.4%

      \[\leadsto x + \color{blue}{b \cdot a} \]

   if -4e114 < (+.f64 x y) < -5.00000000000000003e40

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in x around inf 66.4%

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

   3. Taylor expanded in a around 0 57.4%

      \[\leadsto x + \color{blue}{-0.5 \cdot b} \]

   if -1.9999999999999999e-48 < (+.f64 x y) < 9.9999999999999998e-17

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.9%

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

   3. Taylor expanded in b around inf 67.5%

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

   if 9.9999999999999998e-17 < (+.f64 x y)

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.8%

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

   3. Taylor expanded in b around 0 81.2%

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

      1. sub-neg 81.2%

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

      2. associate-+r+ 81.2%

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

      3. associate-+r+ 81.2%

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

      4. *-rgt-identity 81.2%

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

      5. distribute-rgt-neg-in 81.2%

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

      6. distribute-lft-in 81.2%

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

      7. sub-neg 81.2%

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

      8. associate-+r+ 81.2%

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

      9. +-commutative 81.2%

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

      10. fma-def 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in z around 0 63.1%

      \[\leadsto \color{blue}{x + y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{+114}:\\ \;\;\;\;x + b \cdot a\\ \mathbf{elif}\;x + y \leq -5 \cdot 10^{+40}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{elif}\;x + y \leq -2 \cdot 10^{-48}:\\ \;\;\;\;x + b \cdot a\\ \mathbf{elif}\;x + y \leq 10^{-16}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 44.0% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot a\\ \mathbf{if}\;x + y \leq -4 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x + y \leq -5 \cdot 10^{+40}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{elif}\;x + y \leq -2 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b a))))
   (if (<= (+ x y) -4e+114)
     t_1
     (if (<= (+ x y) -5e+40)
       (+ x (* -0.5 b))
       (if (<= (+ x y) -2e-48)
         t_1
         (if (<= (+ x y) 2e-22) (* b (- a 0.5)) (+ y (* -0.5 b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * a);
	double tmp;
	if ((x + y) <= -4e+114) {
		tmp = t_1;
	} else if ((x + y) <= -5e+40) {
		tmp = x + (-0.5 * b);
	} else if ((x + y) <= -2e-48) {
		tmp = t_1;
	} else if ((x + y) <= 2e-22) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * a)
    if ((x + y) <= (-4d+114)) then
        tmp = t_1
    else if ((x + y) <= (-5d+40)) then
        tmp = x + ((-0.5d0) * b)
    else if ((x + y) <= (-2d-48)) then
        tmp = t_1
    else if ((x + y) <= 2d-22) then
        tmp = b * (a - 0.5d0)
    else
        tmp = y + ((-0.5d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * a);
	double tmp;
	if ((x + y) <= -4e+114) {
		tmp = t_1;
	} else if ((x + y) <= -5e+40) {
		tmp = x + (-0.5 * b);
	} else if ((x + y) <= -2e-48) {
		tmp = t_1;
	} else if ((x + y) <= 2e-22) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * a)
	tmp = 0
	if (x + y) <= -4e+114:
		tmp = t_1
	elif (x + y) <= -5e+40:
		tmp = x + (-0.5 * b)
	elif (x + y) <= -2e-48:
		tmp = t_1
	elif (x + y) <= 2e-22:
		tmp = b * (a - 0.5)
	else:
		tmp = y + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * a))
	tmp = 0.0
	if (Float64(x + y) <= -4e+114)
		tmp = t_1;
	elseif (Float64(x + y) <= -5e+40)
		tmp = Float64(x + Float64(-0.5 * b));
	elseif (Float64(x + y) <= -2e-48)
		tmp = t_1;
	elseif (Float64(x + y) <= 2e-22)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(y + Float64(-0.5 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * a);
	tmp = 0.0;
	if ((x + y) <= -4e+114)
		tmp = t_1;
	elseif ((x + y) <= -5e+40)
		tmp = x + (-0.5 * b);
	elseif ((x + y) <= -2e-48)
		tmp = t_1;
	elseif ((x + y) <= 2e-22)
		tmp = b * (a - 0.5);
	else
		tmp = y + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -4e+114], t$95$1, If[LessEqual[N[(x + y), $MachinePrecision], -5e+40], N[(x + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], -2e-48], t$95$1, If[LessEqual[N[(x + y), $MachinePrecision], 2e-22], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x y) < -4e114 or -5.00000000000000003e40 < (+.f64 x y) < -1.9999999999999999e-48

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in x around inf 54.0%

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

   3. Taylor expanded in a around inf 46.4%

      \[\leadsto x + \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative 46.4%

         \[\leadsto x + \color{blue}{b \cdot a} \]

   5. Simplified 46.4%

      \[\leadsto x + \color{blue}{b \cdot a} \]

   if -4e114 < (+.f64 x y) < -5.00000000000000003e40

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in x around inf 66.4%

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

   3. Taylor expanded in a around 0 57.4%

      \[\leadsto x + \color{blue}{-0.5 \cdot b} \]

   if -1.9999999999999999e-48 < (+.f64 x y) < 2.0000000000000001e-22

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.9%

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

   3. Taylor expanded in b around inf 67.0%

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

   if 2.0000000000000001e-22 < (+.f64 x y)

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in y around inf 45.6%

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

   3. Taylor expanded in a around 0 34.1%

      \[\leadsto y + \color{blue}{-0.5 \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{+114}:\\ \;\;\;\;x + b \cdot a\\ \mathbf{elif}\;x + y \leq -5 \cdot 10^{+40}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{elif}\;x + y \leq -2 \cdot 10^{-48}:\\ \;\;\;\;x + b \cdot a\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \]

Alternative 11: 48.9% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot a\\ \mathbf{if}\;x + y \leq -4 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x + y \leq -5 \cdot 10^{+40}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{elif}\;x + y \leq -2 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x + y \leq 10^{-16}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b a))))
   (if (<= (+ x y) -4e+114)
     t_1
     (if (<= (+ x y) -5e+40)
       (+ x (* -0.5 b))
       (if (<= (+ x y) -2e-48)
         t_1
         (if (<= (+ x y) 1e-16) (* b (- a 0.5)) (+ y (* b a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * a);
	double tmp;
	if ((x + y) <= -4e+114) {
		tmp = t_1;
	} else if ((x + y) <= -5e+40) {
		tmp = x + (-0.5 * b);
	} else if ((x + y) <= -2e-48) {
		tmp = t_1;
	} else if ((x + y) <= 1e-16) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y + (b * 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) :: t_1
    real(8) :: tmp
    t_1 = x + (b * a)
    if ((x + y) <= (-4d+114)) then
        tmp = t_1
    else if ((x + y) <= (-5d+40)) then
        tmp = x + ((-0.5d0) * b)
    else if ((x + y) <= (-2d-48)) then
        tmp = t_1
    else if ((x + y) <= 1d-16) then
        tmp = b * (a - 0.5d0)
    else
        tmp = y + (b * 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 t_1 = x + (b * a);
	double tmp;
	if ((x + y) <= -4e+114) {
		tmp = t_1;
	} else if ((x + y) <= -5e+40) {
		tmp = x + (-0.5 * b);
	} else if ((x + y) <= -2e-48) {
		tmp = t_1;
	} else if ((x + y) <= 1e-16) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y + (b * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * a)
	tmp = 0
	if (x + y) <= -4e+114:
		tmp = t_1
	elif (x + y) <= -5e+40:
		tmp = x + (-0.5 * b)
	elif (x + y) <= -2e-48:
		tmp = t_1
	elif (x + y) <= 1e-16:
		tmp = b * (a - 0.5)
	else:
		tmp = y + (b * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * a))
	tmp = 0.0
	if (Float64(x + y) <= -4e+114)
		tmp = t_1;
	elseif (Float64(x + y) <= -5e+40)
		tmp = Float64(x + Float64(-0.5 * b));
	elseif (Float64(x + y) <= -2e-48)
		tmp = t_1;
	elseif (Float64(x + y) <= 1e-16)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(y + Float64(b * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * a);
	tmp = 0.0;
	if ((x + y) <= -4e+114)
		tmp = t_1;
	elseif ((x + y) <= -5e+40)
		tmp = x + (-0.5 * b);
	elseif ((x + y) <= -2e-48)
		tmp = t_1;
	elseif ((x + y) <= 1e-16)
		tmp = b * (a - 0.5);
	else
		tmp = y + (b * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -4e+114], t$95$1, If[LessEqual[N[(x + y), $MachinePrecision], -5e+40], N[(x + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], -2e-48], t$95$1, If[LessEqual[N[(x + y), $MachinePrecision], 1e-16], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x y) < -4e114 or -5.00000000000000003e40 < (+.f64 x y) < -1.9999999999999999e-48

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in x around inf 54.0%

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

   3. Taylor expanded in a around inf 46.4%

      \[\leadsto x + \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative 46.4%

         \[\leadsto x + \color{blue}{b \cdot a} \]

   5. Simplified 46.4%

      \[\leadsto x + \color{blue}{b \cdot a} \]

   if -4e114 < (+.f64 x y) < -5.00000000000000003e40

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in x around inf 66.4%

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

   3. Taylor expanded in a around 0 57.4%

      \[\leadsto x + \color{blue}{-0.5 \cdot b} \]

   if -1.9999999999999999e-48 < (+.f64 x y) < 9.9999999999999998e-17

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.9%

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

   3. Taylor expanded in b around inf 67.5%

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

   if 9.9999999999999998e-17 < (+.f64 x y)

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in y around inf 44.9%

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

   3. Taylor expanded in a around inf 37.9%

      \[\leadsto y + \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative 49.3%

         \[\leadsto x + \color{blue}{b \cdot a} \]

   5. Simplified 37.9%

      \[\leadsto y + \color{blue}{b \cdot a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{+114}:\\ \;\;\;\;x + b \cdot a\\ \mathbf{elif}\;x + y \leq -5 \cdot 10^{+40}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{elif}\;x + y \leq -2 \cdot 10^{-48}:\\ \;\;\;\;x + b \cdot a\\ \mathbf{elif}\;x + y \leq 10^{-16}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot a\\ \end{array} \]

Alternative 12: 54.3% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+181}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq 10^{-16}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -5e+181)
   (+ x y)
   (if (<= (+ x y) 1e-16) (* b (- a 0.5)) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -5e+181) {
		tmp = x + y;
	} else if ((x + y) <= 1e-16) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + 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 ((x + y) <= (-5d+181)) then
        tmp = x + y
    else if ((x + y) <= 1d-16) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x + 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 ((x + y) <= -5e+181) {
		tmp = x + y;
	} else if ((x + y) <= 1e-16) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -5e+181:
		tmp = x + y
	elif (x + y) <= 1e-16:
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -5e+181)
		tmp = Float64(x + y);
	elseif (Float64(x + y) <= 1e-16)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -5e+181)
		tmp = x + y;
	elseif ((x + y) <= 1e-16)
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e+181], N[(x + y), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 1e-16], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -5.0000000000000003e181 or 9.9999999999999998e-17 < (+.f64 x y)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.9%

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

   3. Taylor expanded in b around 0 80.8%

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

      1. sub-neg 80.8%

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

      2. associate-+r+ 80.8%

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

      3. associate-+r+ 80.8%

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

      4. *-rgt-identity 80.8%

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

      5. distribute-rgt-neg-in 80.8%

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

      6. distribute-lft-in 80.9%

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

      7. sub-neg 80.9%

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

      8. associate-+r+ 80.9%

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

      9. +-commutative 80.9%

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

      10. fma-def 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in z around 0 70.0%

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

   if -5.0000000000000003e181 < (+.f64 x y) < 9.9999999999999998e-17

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.8%

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

   3. Taylor expanded in b around inf 59.4%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+181}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq 10^{-16}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13: 48.6% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+173}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{elif}\;x + y \leq 10^{-16}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -1e+173)
   (+ x (* -0.5 b))
   (if (<= (+ x y) 1e-16) (* b (- a 0.5)) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -1e+173) {
		tmp = x + (-0.5 * b);
	} else if ((x + y) <= 1e-16) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + 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 ((x + y) <= (-1d+173)) then
        tmp = x + ((-0.5d0) * b)
    else if ((x + y) <= 1d-16) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x + 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 ((x + y) <= -1e+173) {
		tmp = x + (-0.5 * b);
	} else if ((x + y) <= 1e-16) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -1e+173:
		tmp = x + (-0.5 * b)
	elif (x + y) <= 1e-16:
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -1e+173)
		tmp = Float64(x + Float64(-0.5 * b));
	elseif (Float64(x + y) <= 1e-16)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -1e+173)
		tmp = x + (-0.5 * b);
	elseif ((x + y) <= 1e-16)
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e+173], N[(x + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 1e-16], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1e173

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in x around inf 50.8%

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

   3. Taylor expanded in a around 0 38.1%

      \[\leadsto x + \color{blue}{-0.5 \cdot b} \]

   if -1e173 < (+.f64 x y) < 9.9999999999999998e-17

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.8%

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

   3. Taylor expanded in b around inf 59.9%

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

   if 9.9999999999999998e-17 < (+.f64 x y)

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.8%

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

   3. Taylor expanded in b around 0 81.2%

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

      1. sub-neg 81.2%

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

      2. associate-+r+ 81.2%

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

      3. associate-+r+ 81.2%

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

      4. *-rgt-identity 81.2%

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

      5. distribute-rgt-neg-in 81.2%

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

      6. distribute-lft-in 81.2%

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

      7. sub-neg 81.2%

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

      8. associate-+r+ 81.2%

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

      9. +-commutative 81.2%

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

      10. fma-def 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in z around 0 63.1%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+173}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{elif}\;x + y \leq 10^{-16}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 14: 58.0% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 10^{-81}:\\ \;\;\;\;x + \left(-0.5 \cdot b + b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 1e-81) (+ x (+ (* -0.5 b) (* b a))) (+ y (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 1e-81) {
		tmp = x + ((-0.5 * b) + (b * a));
	} else {
		tmp = y + (b * (a - 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) :: tmp
    if ((x + y) <= 1d-81) then
        tmp = x + (((-0.5d0) * b) + (b * a))
    else
        tmp = y + (b * (a - 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 tmp;
	if ((x + y) <= 1e-81) {
		tmp = x + ((-0.5 * b) + (b * a));
	} else {
		tmp = y + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= 1e-81:
		tmp = x + ((-0.5 * b) + (b * a))
	else:
		tmp = y + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= 1e-81)
		tmp = Float64(x + Float64(Float64(-0.5 * b) + Float64(b * a)));
	else
		tmp = Float64(y + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= 1e-81)
		tmp = x + ((-0.5 * b) + (b * a));
	else
		tmp = y + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 1e-81], N[(x + N[(N[(-0.5 * b), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 9.9999999999999996e-82

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in x around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. sub-neg 58.0%

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

      3. distribute-lft-in 58.1%

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

      4. metadata-eval 58.1%

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

   4. Applied egg-rr 58.1%

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

   if 9.9999999999999996e-82 < (+.f64 x y)

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in y around inf 50.5%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{-81}:\\ \;\;\;\;x + \left(-0.5 \cdot b + b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 15: 46.9% accurate, 10.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{+169}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -2e+169) (+ x y) (if (<= (+ x y) 2e-22) (* b a) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -2e+169) {
		tmp = x + y;
	} else if ((x + y) <= 2e-22) {
		tmp = b * a;
	} else {
		tmp = x + 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 ((x + y) <= (-2d+169)) then
        tmp = x + y
    else if ((x + y) <= 2d-22) then
        tmp = b * a
    else
        tmp = x + 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 ((x + y) <= -2e+169) {
		tmp = x + y;
	} else if ((x + y) <= 2e-22) {
		tmp = b * a;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -2e+169:
		tmp = x + y
	elif (x + y) <= 2e-22:
		tmp = b * a
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -2e+169)
		tmp = Float64(x + y);
	elseif (Float64(x + y) <= 2e-22)
		tmp = Float64(b * a);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -2e+169)
		tmp = x + y;
	elseif ((x + y) <= 2e-22)
		tmp = b * a;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -2e+169], N[(x + y), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 2e-22], N[(b * a), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.99999999999999987e169 or 2.0000000000000001e-22 < (+.f64 x y)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.9%

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

   3. Taylor expanded in b around 0 78.9%

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

      1. sub-neg 78.9%

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

      2. associate-+r+ 78.9%

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

      3. associate-+r+ 78.9%

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

      4. *-rgt-identity 78.9%

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

      5. distribute-rgt-neg-in 78.9%

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

      6. distribute-lft-in 78.9%

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

      7. sub-neg 78.9%

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

      8. associate-+r+ 78.9%

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

      9. +-commutative 78.9%

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

      10. fma-def 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in z around 0 67.8%

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

   if -1.99999999999999987e169 < (+.f64 x y) < 2.0000000000000001e-22

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.8%

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

   3. Taylor expanded in a around inf 41.3%

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative 41.3%

         \[\leadsto \color{blue}{b \cdot a} \]

   5. Simplified 41.3%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{+169}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 16: 54.4% accurate, 10.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 10^{-16}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 1e-16) (+ x (* b (- a 0.5))) (+ y (* b a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 1e-16) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (b * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x + y) <= 1d-16) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = y + (b * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 1e-16) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (b * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= 1e-16:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = y + (b * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= 1e-16)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(y + Float64(b * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= 1e-16)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y + (b * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 1e-16], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 9.9999999999999998e-17

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in x around inf 60.0%

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

   if 9.9999999999999998e-17 < (+.f64 x y)

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in y around inf 44.9%

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

   3. Taylor expanded in a around inf 37.9%

      \[\leadsto y + \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative 49.3%

         \[\leadsto x + \color{blue}{b \cdot a} \]

   5. Simplified 37.9%

      \[\leadsto y + \color{blue}{b \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{-16}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot a\\ \end{array} \]

Alternative 17: 58.0% accurate, 10.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq 10^{-81}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= (+ x y) 1e-81) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= 1e-81) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= 1d-81) then
        tmp = x + t_1
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= 1e-81) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= 1e-81:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= 1e-81)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= 1e-81)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], 1e-81], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 9.9999999999999996e-82

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in x around inf 58.0%

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

   if 9.9999999999999996e-82 < (+.f64 x y)

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in y around inf 50.5%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{-81}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 18: 78.6% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

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 + y) + (b * (a - 0.5d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

2. Taylor expanded in z around 0 79.7%

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

   1. +-commutative 79.7%

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

4. Simplified 79.7%

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

5. Final simplification 79.7%

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

Alternative 19: 28.1% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3700000:\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.2e-275) x (if (<= y 3700000.0) (* b a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.2e-275) {
		tmp = x;
	} else if (y <= 3700000.0) {
		tmp = b * a;
	} else {
		tmp = 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 (y <= (-9.2d-275)) then
        tmp = x
    else if (y <= 3700000.0d0) then
        tmp = b * a
    else
        tmp = 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 (y <= -9.2e-275) {
		tmp = x;
	} else if (y <= 3700000.0) {
		tmp = b * a;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.2e-275:
		tmp = x
	elif y <= 3700000.0:
		tmp = b * a
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.2e-275)
		tmp = x;
	elseif (y <= 3700000.0)
		tmp = Float64(b * a);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9.2e-275)
		tmp = x;
	elseif (y <= 3700000.0)
		tmp = b * a;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.2e-275], x, If[LessEqual[y, 3700000.0], N[(b * a), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < -9.19999999999999959e-275

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.9%

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

   3. Taylor expanded in x around inf 25.9%

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

   if -9.19999999999999959e-275 < y < 3.7e6

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.9%

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

   3. Taylor expanded in a around inf 36.2%

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative 36.2%

         \[\leadsto \color{blue}{b \cdot a} \]

   5. Simplified 36.2%

      \[\leadsto \color{blue}{b \cdot a} \]

   if 3.7e6 < y

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.8%

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

   3. Taylor expanded in y around inf 47.3%

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

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3700000:\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 20: 28.7% accurate, 37.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -8.4e+71) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.4e+71) {
		tmp = x;
	} else {
		tmp = 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 (x <= (-8.4d+71)) then
        tmp = x
    else
        tmp = 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 (x <= -8.4e+71) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.4e+71:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.4e+71)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.4e+71)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.4e+71], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -8.39999999999999957e71

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 100.0%

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

   3. Taylor expanded in x around inf 47.1%

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

   if -8.39999999999999957e71 < x

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around 0 99.8%

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

   3. Taylor expanded in y around inf 25.3%

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

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 21: 21.6% accurate, 115.0× 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 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

2. Taylor expanded in a around 0 99.9%

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

3. Taylor expanded in x around inf 22.9%

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

4. Final simplification 22.9%

   \[\leadsto x \]

Developer target: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y\right) + \frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t))))
  (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + y) + (((1.0 - pow(log(t), 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * 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 + y) + (((1.0d0 - (log(t) ** 2.0d0)) * z) / (1.0d0 + log(t)))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x + y) + (((1.0 - Math.pow(Math.log(t), 2.0)) * z) / (1.0 + Math.log(t)))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + y) + (((1.0 - math.pow(math.log(t), 2.0)) * z) / (1.0 + math.log(t)))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + y) + Float64(Float64(Float64(1.0 - (log(t) ^ 2.0)) * z) / Float64(1.0 + log(t)))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + y) + (((1.0 - (log(t) ^ 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + y), $MachinePrecision] + N[(N[(N[(1.0 - N[Power[N[Log[t], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] / N[(1.0 + N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))