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

Percentage Accurate: 99.9% → 99.9%

Time: 10.3s

Alternatives: 12

Speedup: 1.0×

• could not determine a ground truth

  1. x = -1.2466534478307259e+73
  2. y = -2.2559975037975945e+74
  3. z = -9.312714371693218e-59
  4. t = 5.3219278334497084e-123
  5. a = 2.497737201752656e-10
  6. b = -3.2205267798236964e-302

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: 99.9% 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: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $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. Add Preprocessing
3. Step-by-step derivation

   1. associate--l+ 99.9%

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

   2. sub-neg 99.9%

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

   3. sub-neg 99.9%

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

   4. *-un-lft-identity 99.9%

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

   5. *-commutative 99.9%

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

   6. distribute-rgt-out-- 99.9%

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

4. Applied egg-rr 99.9%

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

5. Final simplification 99.9%

   \[\leadsto \left(z \cdot \left(1 - \log t\right) + \left(x + y\right)\right) + \left(a - 0.5\right) \cdot b \]
6. Add Preprocessing

Alternative 2: 92.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+120} \lor \neg \left(z \leq 5.4 \cdot 10^{+149}\right):\\ \;\;\;\;t\_1 + \left(z + \left(y - z \cdot \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= z -2.35e+120) (not (<= z 5.4e+149)))
     (+ t_1 (+ z (- y (* z (log t)))))
     (+ t_1 (+ x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((z <= -2.35e+120) || !(z <= 5.4e+149)) {
		tmp = t_1 + (z + (y - (z * log(t))));
	} else {
		tmp = t_1 + (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 = (a - 0.5d0) * b
    if ((z <= (-2.35d+120)) .or. (.not. (z <= 5.4d+149))) then
        tmp = t_1 + (z + (y - (z * log(t))))
    else
        tmp = t_1 + (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 = (a - 0.5) * b;
	double tmp;
	if ((z <= -2.35e+120) || !(z <= 5.4e+149)) {
		tmp = t_1 + (z + (y - (z * Math.log(t))));
	} else {
		tmp = t_1 + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (z <= -2.35e+120) or not (z <= 5.4e+149):
		tmp = t_1 + (z + (y - (z * math.log(t))))
	else:
		tmp = t_1 + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((z <= -2.35e+120) || !(z <= 5.4e+149))
		tmp = Float64(t_1 + Float64(z + Float64(y - Float64(z * log(t)))));
	else
		tmp = Float64(t_1 + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if ((z <= -2.35e+120) || ~((z <= 5.4e+149)))
		tmp = t_1 + (z + (y - (z * log(t))));
	else
		tmp = t_1 + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[z, -2.35e+120], N[Not[LessEqual[z, 5.4e+149]], $MachinePrecision]], N[(t$95$1 + N[(z + N[(y - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.34999999999999997e120 or 5.4000000000000002e149 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 94.6%

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

      1. +-commutative 94.6%

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

      2. associate--l+ 94.6%

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

   5. Simplified 94.6%

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

   if -2.34999999999999997e120 < z < 5.4000000000000002e149

   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. Add Preprocessing

   3. Taylor expanded in z around 0 95.2%

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

      1. +-commutative 95.2%

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

   5. Simplified 95.2%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+120} \lor \neg \left(z \leq 5.4 \cdot 10^{+149}\right):\\ \;\;\;\;\left(a - 0.5\right) \cdot b + \left(z + \left(y - z \cdot \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+148} \lor \neg \left(z \leq 1.65 \cdot 10^{+151}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= z -1.85e+148) (not (<= z 1.65e+151)))
     (+ (* z (- 1.0 (log t))) t_1)
     (+ t_1 (+ x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((z <= -1.85e+148) || !(z <= 1.65e+151)) {
		tmp = (z * (1.0 - log(t))) + t_1;
	} else {
		tmp = t_1 + (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 = (a - 0.5d0) * b
    if ((z <= (-1.85d+148)) .or. (.not. (z <= 1.65d+151))) then
        tmp = (z * (1.0d0 - log(t))) + t_1
    else
        tmp = t_1 + (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 = (a - 0.5) * b;
	double tmp;
	if ((z <= -1.85e+148) || !(z <= 1.65e+151)) {
		tmp = (z * (1.0 - Math.log(t))) + t_1;
	} else {
		tmp = t_1 + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (z <= -1.85e+148) or not (z <= 1.65e+151):
		tmp = (z * (1.0 - math.log(t))) + t_1
	else:
		tmp = t_1 + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((z <= -1.85e+148) || !(z <= 1.65e+151))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + t_1);
	else
		tmp = Float64(t_1 + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if ((z <= -1.85e+148) || ~((z <= 1.65e+151)))
		tmp = (z * (1.0 - log(t))) + t_1;
	else
		tmp = t_1 + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[z, -1.85e+148], N[Not[LessEqual[z, 1.65e+151]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8500000000000001e148 or 1.65000000000000012e151 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 94.1%

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

      1. +-commutative 94.1%

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

      2. associate--l+ 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in z around inf 87.9%

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

   if -1.8500000000000001e148 < z < 1.65000000000000012e151

   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. Add Preprocessing

   3. Taylor expanded in z around 0 94.5%

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

      1. +-commutative 94.5%

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

   5. Simplified 94.5%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+148} \lor \neg \left(z \leq 1.65 \cdot 10^{+151}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+120} \lor \neg \left(z \leq 3.5 \cdot 10^{+203}\right):\\ \;\;\;\;a \cdot b + \left(z + \left(y - z \cdot \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.2e+120) (not (<= z 3.5e+203)))
   (+ (* a b) (+ z (- y (* z (log t)))))
   (+ (* (- a 0.5) b) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e+120) || !(z <= 3.5e+203)) {
		tmp = (a * b) + (z + (y - (z * log(t))));
	} else {
		tmp = ((a - 0.5) * b) + (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 ((z <= (-4.2d+120)) .or. (.not. (z <= 3.5d+203))) then
        tmp = (a * b) + (z + (y - (z * log(t))))
    else
        tmp = ((a - 0.5d0) * b) + (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 ((z <= -4.2e+120) || !(z <= 3.5e+203)) {
		tmp = (a * b) + (z + (y - (z * Math.log(t))));
	} else {
		tmp = ((a - 0.5) * b) + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.2e+120) or not (z <= 3.5e+203):
		tmp = (a * b) + (z + (y - (z * math.log(t))))
	else:
		tmp = ((a - 0.5) * b) + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.2e+120) || !(z <= 3.5e+203))
		tmp = Float64(Float64(a * b) + Float64(z + Float64(y - Float64(z * log(t)))));
	else
		tmp = Float64(Float64(Float64(a - 0.5) * b) + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.2e+120) || ~((z <= 3.5e+203)))
		tmp = (a * b) + (z + (y - (z * log(t))));
	else
		tmp = ((a - 0.5) * b) + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.2e+120], N[Not[LessEqual[z, 3.5e+203]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(z + N[(y - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000001e120 or 3.50000000000000031e203 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 96.6%

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

      1. +-commutative 96.6%

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

      2. associate--l+ 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in a around inf 91.6%

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

      1. *-commutative 22.7%

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

   8. Simplified 91.6%

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

   if -4.2000000000000001e120 < z < 3.50000000000000031e203

   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. Add Preprocessing

   3. Taylor expanded in z around 0 93.8%

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

      1. +-commutative 93.8%

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

   5. Simplified 93.8%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+120} \lor \neg \left(z \leq 3.5 \cdot 10^{+203}\right):\\ \;\;\;\;a \cdot b + \left(z + \left(y - z \cdot \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -400000000:\\ \;\;\;\;\left(z \cdot \left(1 - \log t\right) + \left(x + y\right)\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b + \left(z + \left(y - z \cdot \log t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -400000000.0)
   (+ (+ (* z (- 1.0 (log t))) (+ x y)) (* a b))
   (+ (* (- a 0.5) b) (+ z (- y (* z (log t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -400000000.0) {
		tmp = ((z * (1.0 - log(t))) + (x + y)) + (a * b);
	} else {
		tmp = ((a - 0.5) * b) + (z + (y - (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 ((x + y) <= (-400000000.0d0)) then
        tmp = ((z * (1.0d0 - log(t))) + (x + y)) + (a * b)
    else
        tmp = ((a - 0.5d0) * b) + (z + (y - (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 ((x + y) <= -400000000.0) {
		tmp = ((z * (1.0 - Math.log(t))) + (x + y)) + (a * b);
	} else {
		tmp = ((a - 0.5) * b) + (z + (y - (z * Math.log(t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -400000000.0:
		tmp = ((z * (1.0 - math.log(t))) + (x + y)) + (a * b)
	else:
		tmp = ((a - 0.5) * b) + (z + (y - (z * math.log(t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -400000000.0)
		tmp = Float64(Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y)) + Float64(a * b));
	else
		tmp = Float64(Float64(Float64(a - 0.5) * b) + Float64(z + Float64(y - Float64(z * log(t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -400000000.0)
		tmp = ((z * (1.0 - log(t))) + (x + y)) + (a * b);
	else
		tmp = ((a - 0.5) * b) + (z + (y - (z * log(t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -400000000.0], N[(N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision] + N[(z + N[(y - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4e8

   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. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. sub-neg 99.9%

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

      4. *-un-lft-identity 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-out-- 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around inf 91.7%

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

      1. *-commutative 49.9%

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

   7. Simplified 91.7%

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

   if -4e8 < (+.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. Add Preprocessing

   3. Taylor expanded in x around 0 86.1%

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

      1. +-commutative 86.1%

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

      2. associate--l+ 86.1%

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

   5. Simplified 86.1%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -400000000:\\ \;\;\;\;\left(z \cdot \left(1 - \log t\right) + \left(x + y\right)\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b + \left(z + \left(y - z \cdot \log t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.0% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+122} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+98}\right):\\ \;\;\;\;y + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= t_1 -1e+122) (not (<= t_1 2e+98)))
     (+ y t_1)
     (+ (+ x y) (* b -0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -1e+122) || !(t_1 <= 2e+98)) {
		tmp = y + t_1;
	} else {
		tmp = (x + y) + (b * -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if ((t_1 <= (-1d+122)) .or. (.not. (t_1 <= 2d+98))) then
        tmp = y + t_1
    else
        tmp = (x + y) + (b * (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -1e+122) || !(t_1 <= 2e+98)) {
		tmp = y + t_1;
	} else {
		tmp = (x + y) + (b * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (t_1 <= -1e+122) or not (t_1 <= 2e+98):
		tmp = y + t_1
	else:
		tmp = (x + y) + (b * -0.5)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((t_1 <= -1e+122) || !(t_1 <= 2e+98))
		tmp = Float64(y + t_1);
	else
		tmp = Float64(Float64(x + y) + Float64(b * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if ((t_1 <= -1e+122) || ~((t_1 <= 2e+98)))
		tmp = y + t_1;
	else
		tmp = (x + y) + (b * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+122], N[Not[LessEqual[t$95$1, 2e+98]], $MachinePrecision]], N[(y + t$95$1), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(b * -0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -1.00000000000000001e122 or 2e98 < (*.f64 (-.f64 a 1/2) b)

   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. Add Preprocessing

   3. Taylor expanded in y around inf 82.7%

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

   if -1.00000000000000001e122 < (*.f64 (-.f64 a 1/2) b) < 2e98

   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. Add Preprocessing

   3. Taylor expanded in z around 0 70.6%

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

      1. +-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in a around 0 67.5%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -1 \cdot 10^{+122} \lor \neg \left(\left(a - 0.5\right) \cdot b \leq 2 \cdot 10^{+98}\right):\\ \;\;\;\;y + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.7% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0004 \lor \neg \left(a \leq 4.7 \cdot 10^{-39}\right):\\ \;\;\;\;a \cdot b + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -0.0004) (not (<= a 4.7e-39)))
   (+ (* a b) (+ x y))
   (+ (+ x y) (* b -0.5))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -0.0004) || !(a <= 4.7e-39)) {
		tmp = (a * b) + (x + y);
	} else {
		tmp = (x + y) + (b * -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 ((a <= (-0.0004d0)) .or. (.not. (a <= 4.7d-39))) then
        tmp = (a * b) + (x + y)
    else
        tmp = (x + y) + (b * (-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 ((a <= -0.0004) || !(a <= 4.7e-39)) {
		tmp = (a * b) + (x + y);
	} else {
		tmp = (x + y) + (b * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -0.0004) or not (a <= 4.7e-39):
		tmp = (a * b) + (x + y)
	else:
		tmp = (x + y) + (b * -0.5)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -0.0004) || !(a <= 4.7e-39))
		tmp = Float64(Float64(a * b) + Float64(x + y));
	else
		tmp = Float64(Float64(x + y) + Float64(b * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -0.0004) || ~((a <= 4.7e-39)))
		tmp = (a * b) + (x + y);
	else
		tmp = (x + y) + (b * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -0.0004], N[Not[LessEqual[a, 4.7e-39]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(b * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.00000000000000019e-4 or 4.7000000000000002e-39 < a

   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. Add Preprocessing

   3. Taylor expanded in z around 0 77.3%

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

      1. +-commutative 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in a around inf 77.2%

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

      1. *-commutative 60.7%

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

   8. Simplified 77.2%

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

   if -4.00000000000000019e-4 < a < 4.7000000000000002e-39

   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. Add Preprocessing

   3. Taylor expanded in z around 0 77.9%

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

      1. +-commutative 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in a around 0 77.9%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0004 \lor \neg \left(a \leq 4.7 \cdot 10^{-39}\right):\\ \;\;\;\;a \cdot b + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.5% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1400000000 \lor \neg \left(a \leq 4.7 \cdot 10^{-39}\right):\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1400000000.0) (not (<= a 4.7e-39)))
   (+ x (* a b))
   (+ x (* b -0.5))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1400000000.0) || !(a <= 4.7e-39)) {
		tmp = x + (a * b);
	} else {
		tmp = x + (b * -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 ((a <= (-1400000000.0d0)) .or. (.not. (a <= 4.7d-39))) then
        tmp = x + (a * b)
    else
        tmp = x + (b * (-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 ((a <= -1400000000.0) || !(a <= 4.7e-39)) {
		tmp = x + (a * b);
	} else {
		tmp = x + (b * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1400000000.0) or not (a <= 4.7e-39):
		tmp = x + (a * b)
	else:
		tmp = x + (b * -0.5)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1400000000.0) || !(a <= 4.7e-39))
		tmp = Float64(x + Float64(a * b));
	else
		tmp = Float64(x + Float64(b * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1400000000.0) || ~((a <= 4.7e-39)))
		tmp = x + (a * b);
	else
		tmp = x + (b * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1400000000.0], N[Not[LessEqual[a, 4.7e-39]], $MachinePrecision]], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4e9 or 4.7000000000000002e-39 < a

   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. Add Preprocessing

   3. Taylor expanded in x around inf 63.8%

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

   4. Taylor expanded in a around inf 63.7%

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

      1. *-commutative 63.7%

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

   6. Simplified 63.7%

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

   if -1.4e9 < a < 4.7000000000000002e-39

   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. Add Preprocessing

   3. Taylor expanded in x around inf 51.6%

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

   4. Taylor expanded in a around 0 51.6%

      \[\leadsto x + \color{blue}{-0.5 \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1400000000 \lor \neg \left(a \leq 4.7 \cdot 10^{-39}\right):\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.5% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;y \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b))) (if (<= y 5.2e+14) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (y <= 5.2e+14) {
		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 = (a - 0.5d0) * b
    if (y <= 5.2d+14) 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 = (a - 0.5) * b;
	double tmp;
	if (y <= 5.2e+14) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if y <= 5.2e+14:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (y <= 5.2e+14)
		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 = (a - 0.5) * b;
	tmp = 0.0;
	if (y <= 5.2e+14)
		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[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[y, 5.2e+14], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 5.2e14

   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. Add Preprocessing

   3. Taylor expanded in x around inf 64.3%

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

   if 5.2e14 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 67.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + \left(a - 0.5\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.8% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Taylor expanded in z around 0 77.6%

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

   1. +-commutative 77.6%

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

5. Simplified 77.6%

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

6. Final simplification 77.6%

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

Alternative 11: 58.6% accurate, 16.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Taylor expanded in x around inf 57.5%

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

4. Final simplification 57.5%

   \[\leadsto x + \left(a - 0.5\right) \cdot b \]
5. Add Preprocessing

Alternative 12: 34.4% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ x + b \cdot -0.5 \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(b * -0.5), $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. Add Preprocessing

3. Taylor expanded in x around inf 57.5%

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

4. Taylor expanded in a around 0 36.9%

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

5. Final simplification 36.9%

   \[\leadsto x + b \cdot -0.5 \]
6. Add Preprocessing

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 2024067 
(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)))