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

Percentage Accurate: 99.9% → 99.9%

Time: 19.2s

Alternatives: 20

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: 99.9% 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

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

FPCore

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

C

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

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 = (y + (x + ((b * a) + (b * (-0.5d0))))) - (z * (log(t) + (-1.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]
7. Add Preprocessing

Alternative 2: 93.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+103}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+144}:\\ \;\;\;\;\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + b \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a - 0.5\right) + \frac{z \cdot \left(1 - \log t\right)}{b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.42e+103)
   (+ (+ y x) (* (- a 0.5) b))
   (if (<= b 2.3e+144)
     (+ (- (+ (+ x y) z) (* z (log t))) (* b a))
     (* b (+ (- a 0.5) (/ (* z (- 1.0 (log t))) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.42e+103) {
		tmp = (y + x) + ((a - 0.5) * b);
	} else if (b <= 2.3e+144) {
		tmp = (((x + y) + z) - (z * log(t))) + (b * a);
	} else {
		tmp = b * ((a - 0.5) + ((z * (1.0 - log(t))) / b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.42d+103)) then
        tmp = (y + x) + ((a - 0.5d0) * b)
    else if (b <= 2.3d+144) then
        tmp = (((x + y) + z) - (z * log(t))) + (b * a)
    else
        tmp = b * ((a - 0.5d0) + ((z * (1.0d0 - log(t))) / b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.42e+103) {
		tmp = (y + x) + ((a - 0.5) * b);
	} else if (b <= 2.3e+144) {
		tmp = (((x + y) + z) - (z * Math.log(t))) + (b * a);
	} else {
		tmp = b * ((a - 0.5) + ((z * (1.0 - Math.log(t))) / b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.42e+103:
		tmp = (y + x) + ((a - 0.5) * b)
	elif b <= 2.3e+144:
		tmp = (((x + y) + z) - (z * math.log(t))) + (b * a)
	else:
		tmp = b * ((a - 0.5) + ((z * (1.0 - math.log(t))) / b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.42e+103)
		tmp = Float64(Float64(y + x) + Float64(Float64(a - 0.5) * b));
	elseif (b <= 2.3e+144)
		tmp = Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(b * a));
	else
		tmp = Float64(b * Float64(Float64(a - 0.5) + Float64(Float64(z * Float64(1.0 - log(t))) / b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.42e+103)
		tmp = (y + x) + ((a - 0.5) * b);
	elseif (b <= 2.3e+144)
		tmp = (((x + y) + z) - (z * log(t))) + (b * a);
	else
		tmp = b * ((a - 0.5) + ((z * (1.0 - log(t))) / b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.42e+103], N[(N[(y + x), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+144], N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a - 0.5), $MachinePrecision] + N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.42e103

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.42e103 < b < 2.3000000000000001e144

   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 a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.3000000000000001e144 < 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. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 88.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;z \leq -9 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) - z \cdot \left(\log t + -1\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+180}:\\ \;\;\;\;\left(y + x\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z - z \cdot \log t\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= z -9e+114)
     (- (* b (- a 0.5)) (* z (+ (log t) -1.0)))
     (if (<= z 7.5e+180) (+ (+ y x) t_1) (+ (- z (* z (log t))) 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 (z <= -9e+114) {
		tmp = (b * (a - 0.5)) - (z * (log(t) + -1.0));
	} else if (z <= 7.5e+180) {
		tmp = (y + x) + t_1;
	} else {
		tmp = (z - (z * log(t))) + 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 (z <= (-9d+114)) then
        tmp = (b * (a - 0.5d0)) - (z * (log(t) + (-1.0d0)))
    else if (z <= 7.5d+180) then
        tmp = (y + x) + t_1
    else
        tmp = (z - (z * log(t))) + 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 (z <= -9e+114) {
		tmp = (b * (a - 0.5)) - (z * (Math.log(t) + -1.0));
	} else if (z <= 7.5e+180) {
		tmp = (y + x) + t_1;
	} else {
		tmp = (z - (z * Math.log(t))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if z <= -9e+114:
		tmp = (b * (a - 0.5)) - (z * (math.log(t) + -1.0))
	elif z <= 7.5e+180:
		tmp = (y + x) + t_1
	else:
		tmp = (z - (z * math.log(t))) + 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 (z <= -9e+114)
		tmp = Float64(Float64(b * Float64(a - 0.5)) - Float64(z * Float64(log(t) + -1.0)));
	elseif (z <= 7.5e+180)
		tmp = Float64(Float64(y + x) + t_1);
	else
		tmp = Float64(Float64(z - Float64(z * log(t))) + 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 (z <= -9e+114)
		tmp = (b * (a - 0.5)) - (z * (log(t) + -1.0));
	elseif (z <= 7.5e+180)
		tmp = (y + x) + t_1;
	else
		tmp = (z - (z * log(t))) + 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[z, -9e+114], N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[Log[t], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+180], N[(N[(y + x), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.0000000000000001e114

   1. Initial program 99.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   if -9.0000000000000001e114 < z < 7.5000000000000003e180

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 7.5000000000000003e180 < z

   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 inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 88.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ t_2 := \left(z - z \cdot \log t\right) + t\_1\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+181}:\\ \;\;\;\;\left(y + x\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)) (t_2 (+ (- z (* z (log t))) t_1)))
   (if (<= z -3.8e+113) t_2 (if (<= z 1.8e+181) (+ (+ y x) t_1) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = (z - (z * log(t))) + t_1;
	double tmp;
	if (z <= -3.8e+113) {
		tmp = t_2;
	} else if (z <= 1.8e+181) {
		tmp = (y + x) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    t_2 = (z - (z * log(t))) + t_1
    if (z <= (-3.8d+113)) then
        tmp = t_2
    else if (z <= 1.8d+181) then
        tmp = (y + x) + t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = (z - (z * Math.log(t))) + t_1;
	double tmp;
	if (z <= -3.8e+113) {
		tmp = t_2;
	} else if (z <= 1.8e+181) {
		tmp = (y + x) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	t_2 = (z - (z * math.log(t))) + t_1
	tmp = 0
	if z <= -3.8e+113:
		tmp = t_2
	elif z <= 1.8e+181:
		tmp = (y + x) + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	t_2 = Float64(Float64(z - Float64(z * log(t))) + t_1)
	tmp = 0.0
	if (z <= -3.8e+113)
		tmp = t_2;
	elseif (z <= 1.8e+181)
		tmp = Float64(Float64(y + x) + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	t_2 = (z - (z * log(t))) + t_1;
	tmp = 0.0;
	if (z <= -3.8e+113)
		tmp = t_2;
	elseif (z <= 1.8e+181)
		tmp = (y + x) + t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[z, -3.8e+113], t$95$2, If[LessEqual[z, 1.8e+181], N[(N[(y + x), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000003e113 or 1.79999999999999992e181 < 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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.8000000000000003e113 < z < 1.79999999999999992e181

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot a - z \cdot \left(\log t + -1\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+189}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* b a) (* z (+ (log t) -1.0)))))
   (if (<= z -7.8e+115)
     t_1
     (if (<= z 1.65e+189) (+ (+ y x) (* (- a 0.5) b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * a) - (z * (log(t) + -1.0));
	double tmp;
	if (z <= -7.8e+115) {
		tmp = t_1;
	} else if (z <= 1.65e+189) {
		tmp = (y + x) + ((a - 0.5) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * a) - (z * (log(t) + (-1.0d0)))
    if (z <= (-7.8d+115)) then
        tmp = t_1
    else if (z <= 1.65d+189) then
        tmp = (y + x) + ((a - 0.5d0) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * a) - (z * (Math.log(t) + -1.0));
	double tmp;
	if (z <= -7.8e+115) {
		tmp = t_1;
	} else if (z <= 1.65e+189) {
		tmp = (y + x) + ((a - 0.5) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * a) - (z * (math.log(t) + -1.0))
	tmp = 0
	if z <= -7.8e+115:
		tmp = t_1
	elif z <= 1.65e+189:
		tmp = (y + x) + ((a - 0.5) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * a) - Float64(z * Float64(log(t) + -1.0)))
	tmp = 0.0
	if (z <= -7.8e+115)
		tmp = t_1;
	elseif (z <= 1.65e+189)
		tmp = Float64(Float64(y + x) + Float64(Float64(a - 0.5) * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * a) - (z * (log(t) + -1.0));
	tmp = 0.0;
	if (z <= -7.8e+115)
		tmp = t_1;
	elseif (z <= 1.65e+189)
		tmp = (y + x) + ((a - 0.5) * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] - N[(z * N[(N[Log[t], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+115], t$95$1, If[LessEqual[z, 1.65e+189], N[(N[(y + x), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.80000000000000012e115 or 1.6500000000000001e189 < z

   1. Initial program 99.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -7.80000000000000012e115 < z < 1.6500000000000001e189

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 83.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+177}:\\ \;\;\;\;x - z \cdot \left(\log t + -1\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+252}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.4e+177)
   (- x (* z (+ (log t) -1.0)))
   (if (<= z 2e+252) (+ (+ y x) (* (- a 0.5) b)) (* z (- 1.0 (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.4e+177) {
		tmp = x - (z * (log(t) + -1.0));
	} else if (z <= 2e+252) {
		tmp = (y + x) + ((a - 0.5) * b);
	} else {
		tmp = z * (1.0 - 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 (z <= (-7.4d+177)) then
        tmp = x - (z * (log(t) + (-1.0d0)))
    else if (z <= 2d+252) then
        tmp = (y + x) + ((a - 0.5d0) * b)
    else
        tmp = z * (1.0d0 - 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 (z <= -7.4e+177) {
		tmp = x - (z * (Math.log(t) + -1.0));
	} else if (z <= 2e+252) {
		tmp = (y + x) + ((a - 0.5) * b);
	} else {
		tmp = z * (1.0 - Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.4e+177:
		tmp = x - (z * (math.log(t) + -1.0))
	elif z <= 2e+252:
		tmp = (y + x) + ((a - 0.5) * b)
	else:
		tmp = z * (1.0 - math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.4e+177)
		tmp = Float64(x - Float64(z * Float64(log(t) + -1.0)));
	elseif (z <= 2e+252)
		tmp = Float64(Float64(y + x) + Float64(Float64(a - 0.5) * b));
	else
		tmp = Float64(z * Float64(1.0 - log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7.4e+177)
		tmp = x - (z * (log(t) + -1.0));
	elseif (z <= 2e+252)
		tmp = (y + x) + ((a - 0.5) * b);
	else
		tmp = z * (1.0 - log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.4e+177], N[(x - N[(z * N[(N[Log[t], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+252], N[(N[(y + x), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.40000000000000028e177

   1. Initial program 99.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -7.40000000000000028e177 < z < 2.0000000000000002e252

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.0000000000000002e252 < z

   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 inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+177}:\\ \;\;\;\;\left(x - z \cdot \log t\right) + z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+252}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.5e+177)
   (+ (- x (* z (log t))) z)
   (if (<= z 2e+252) (+ (+ y x) (* (- a 0.5) b)) (* z (- 1.0 (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.5e+177) {
		tmp = (x - (z * log(t))) + z;
	} else if (z <= 2e+252) {
		tmp = (y + x) + ((a - 0.5) * b);
	} else {
		tmp = z * (1.0 - 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 (z <= (-1.5d+177)) then
        tmp = (x - (z * log(t))) + z
    else if (z <= 2d+252) then
        tmp = (y + x) + ((a - 0.5d0) * b)
    else
        tmp = z * (1.0d0 - 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 (z <= -1.5e+177) {
		tmp = (x - (z * Math.log(t))) + z;
	} else if (z <= 2e+252) {
		tmp = (y + x) + ((a - 0.5) * b);
	} else {
		tmp = z * (1.0 - Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.5e+177:
		tmp = (x - (z * math.log(t))) + z
	elif z <= 2e+252:
		tmp = (y + x) + ((a - 0.5) * b)
	else:
		tmp = z * (1.0 - math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.5e+177)
		tmp = Float64(Float64(x - Float64(z * log(t))) + z);
	elseif (z <= 2e+252)
		tmp = Float64(Float64(y + x) + Float64(Float64(a - 0.5) * b));
	else
		tmp = Float64(z * Float64(1.0 - log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.5e+177)
		tmp = (x - (z * log(t))) + z;
	elseif (z <= 2e+252)
		tmp = (y + x) + ((a - 0.5) * b);
	else
		tmp = z * (1.0 - log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.5e+177], N[(N[(x - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[z, 2e+252], N[(N[(y + x), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e177

   1. Initial program 99.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]

   if -1.5e177 < z < 2.0000000000000002e252

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.0000000000000002e252 < z

   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 inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+253}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -1.4e+178)
     t_1
     (if (<= z 3e+253) (+ (+ y x) (* (- a 0.5) b)) 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 <= -1.4e+178) {
		tmp = t_1;
	} else if (z <= 3e+253) {
		tmp = (y + x) + ((a - 0.5) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    if (z <= (-1.4d+178)) then
        tmp = t_1
    else if (z <= 3d+253) then
        tmp = (y + x) + ((a - 0.5d0) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -1.4e+178) {
		tmp = t_1;
	} else if (z <= 3e+253) {
		tmp = (y + x) + ((a - 0.5) * b);
	} else {
		tmp = 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 <= -1.4e+178:
		tmp = t_1
	elif z <= 3e+253:
		tmp = (y + x) + ((a - 0.5) * b)
	else:
		tmp = 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 <= -1.4e+178)
		tmp = t_1;
	elseif (z <= 3e+253)
		tmp = Float64(Float64(y + x) + Float64(Float64(a - 0.5) * b));
	else
		tmp = 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 <= -1.4e+178)
		tmp = t_1;
	elseif (z <= 3e+253)
		tmp = (y + x) + ((a - 0.5) * b);
	else
		tmp = 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, -1.4e+178], t$95$1, If[LessEqual[z, 3e+253], N[(N[(y + x), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999997e178 or 2.9999999999999998e253 < z

   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. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.39999999999999997e178 < z < 2.9999999999999998e253

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = (y + (x + ((a - 0.5d0) * b))) - (z * (log(t) + (-1.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing
5. Add Preprocessing

Alternative 10: 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]

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. Add Preprocessing

Alternative 11: 61.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{+65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+144}:\\ \;\;\;\;x + b \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= b -6.8e+102)
     t_1
     (if (<= b -1.2e+65)
       (+ x y)
       (if (<= b -2.7e+23)
         t_1
         (if (<= b 1.9e-10)
           (+ x y)
           (if (<= b 1.85e+144) (+ x (* b a)) 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 (b <= -6.8e+102) {
		tmp = t_1;
	} else if (b <= -1.2e+65) {
		tmp = x + y;
	} else if (b <= -2.7e+23) {
		tmp = t_1;
	} else if (b <= 1.9e-10) {
		tmp = x + y;
	} else if (b <= 1.85e+144) {
		tmp = x + (b * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (b <= (-6.8d+102)) then
        tmp = t_1
    else if (b <= (-1.2d+65)) then
        tmp = x + y
    else if (b <= (-2.7d+23)) then
        tmp = t_1
    else if (b <= 1.9d-10) then
        tmp = x + y
    else if (b <= 1.85d+144) then
        tmp = x + (b * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (b <= -6.8e+102) {
		tmp = t_1;
	} else if (b <= -1.2e+65) {
		tmp = x + y;
	} else if (b <= -2.7e+23) {
		tmp = t_1;
	} else if (b <= 1.9e-10) {
		tmp = x + y;
	} else if (b <= 1.85e+144) {
		tmp = x + (b * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if b <= -6.8e+102:
		tmp = t_1
	elif b <= -1.2e+65:
		tmp = x + y
	elif b <= -2.7e+23:
		tmp = t_1
	elif b <= 1.9e-10:
		tmp = x + y
	elif b <= 1.85e+144:
		tmp = x + (b * a)
	else:
		tmp = 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 (b <= -6.8e+102)
		tmp = t_1;
	elseif (b <= -1.2e+65)
		tmp = Float64(x + y);
	elseif (b <= -2.7e+23)
		tmp = t_1;
	elseif (b <= 1.9e-10)
		tmp = Float64(x + y);
	elseif (b <= 1.85e+144)
		tmp = Float64(x + Float64(b * a));
	else
		tmp = 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 (b <= -6.8e+102)
		tmp = t_1;
	elseif (b <= -1.2e+65)
		tmp = x + y;
	elseif (b <= -2.7e+23)
		tmp = t_1;
	elseif (b <= 1.9e-10)
		tmp = x + y;
	elseif (b <= 1.85e+144)
		tmp = x + (b * a);
	else
		tmp = 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[b, -6.8e+102], t$95$1, If[LessEqual[b, -1.2e+65], N[(x + y), $MachinePrecision], If[LessEqual[b, -2.7e+23], t$95$1, If[LessEqual[b, 1.9e-10], N[(x + y), $MachinePrecision], If[LessEqual[b, 1.85e+144], N[(x + N[(b * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.8000000000000001e102 or -1.2000000000000001e65 < b < -2.6999999999999999e23 or 1.8499999999999998e144 < 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. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.8000000000000001e102 < b < -1.2000000000000001e65 or -2.6999999999999999e23 < b < 1.8999999999999999e-10

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 1.8999999999999999e-10 < b < 1.8499999999999998e144

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 61.2% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+31}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= b -8.5e+102)
     t_1
     (if (<= b -3.2e+65)
       (+ x y)
       (if (<= b -4.5e+24) t_1 (if (<= b 1.7e+31) (+ x 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 (b <= -8.5e+102) {
		tmp = t_1;
	} else if (b <= -3.2e+65) {
		tmp = x + y;
	} else if (b <= -4.5e+24) {
		tmp = t_1;
	} else if (b <= 1.7e+31) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (b <= (-8.5d+102)) then
        tmp = t_1
    else if (b <= (-3.2d+65)) then
        tmp = x + y
    else if (b <= (-4.5d+24)) then
        tmp = t_1
    else if (b <= 1.7d+31) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (b <= -8.5e+102) {
		tmp = t_1;
	} else if (b <= -3.2e+65) {
		tmp = x + y;
	} else if (b <= -4.5e+24) {
		tmp = t_1;
	} else if (b <= 1.7e+31) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if b <= -8.5e+102:
		tmp = t_1
	elif b <= -3.2e+65:
		tmp = x + y
	elif b <= -4.5e+24:
		tmp = t_1
	elif b <= 1.7e+31:
		tmp = x + y
	else:
		tmp = 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 (b <= -8.5e+102)
		tmp = t_1;
	elseif (b <= -3.2e+65)
		tmp = Float64(x + y);
	elseif (b <= -4.5e+24)
		tmp = t_1;
	elseif (b <= 1.7e+31)
		tmp = Float64(x + y);
	else
		tmp = 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 (b <= -8.5e+102)
		tmp = t_1;
	elseif (b <= -3.2e+65)
		tmp = x + y;
	elseif (b <= -4.5e+24)
		tmp = t_1;
	elseif (b <= 1.7e+31)
		tmp = x + y;
	else
		tmp = 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[b, -8.5e+102], t$95$1, If[LessEqual[b, -3.2e+65], N[(x + y), $MachinePrecision], If[LessEqual[b, -4.5e+24], t$95$1, If[LessEqual[b, 1.7e+31], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.4999999999999996e102 or -3.20000000000000007e65 < b < -4.50000000000000019e24 or 1.6999999999999999e31 < 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. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -8.4999999999999996e102 < b < -3.20000000000000007e65 or -4.50000000000000019e24 < b < 1.6999999999999999e31

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 50.7% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-5}:\\ \;\;\;\;x + b \cdot a\\ \mathbf{elif}\;x + y \leq 10^{+28}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -4e-5)
   (+ x (* b a))
   (if (<= (+ x y) 1e+28) (* 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) <= -4e-5) {
		tmp = x + (b * a);
	} else if ((x + y) <= 1e+28) {
		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) :: tmp
    if ((x + y) <= (-4d-5)) then
        tmp = x + (b * a)
    else if ((x + y) <= 1d+28) 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 tmp;
	if ((x + y) <= -4e-5) {
		tmp = x + (b * a);
	} else if ((x + y) <= 1e+28) {
		tmp = 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) <= -4e-5:
		tmp = x + (b * a)
	elif (x + y) <= 1e+28:
		tmp = 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) <= -4e-5)
		tmp = Float64(x + Float64(b * a));
	elseif (Float64(x + y) <= 1e+28)
		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)
	tmp = 0.0;
	if ((x + y) <= -4e-5)
		tmp = x + (b * a);
	elseif ((x + y) <= 1e+28)
		tmp = 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], -4e-5], N[(x + N[(b * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 1e+28], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -4.00000000000000033e-5

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -4.00000000000000033e-5 < (+.f64 x y) < 9.99999999999999958e27

   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 b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 9.99999999999999958e27 < (+.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 y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 36.4% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+21}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-204}:\\ \;\;\;\;y\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.8e+21)
   (* b a)
   (if (<= b -3e-204) y (if (<= b 4.9e-26) x (* b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.8e+21) {
		tmp = b * a;
	} else if (b <= -3e-204) {
		tmp = y;
	} else if (b <= 4.9e-26) {
		tmp = x;
	} else {
		tmp = 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 (b <= (-7.8d+21)) then
        tmp = b * a
    else if (b <= (-3d-204)) then
        tmp = y
    else if (b <= 4.9d-26) then
        tmp = x
    else
        tmp = 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 (b <= -7.8e+21) {
		tmp = b * a;
	} else if (b <= -3e-204) {
		tmp = y;
	} else if (b <= 4.9e-26) {
		tmp = x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.8e+21:
		tmp = b * a
	elif b <= -3e-204:
		tmp = y
	elif b <= 4.9e-26:
		tmp = x
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.8e+21)
		tmp = Float64(b * a);
	elseif (b <= -3e-204)
		tmp = y;
	elseif (b <= 4.9e-26)
		tmp = x;
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.8e+21)
		tmp = b * a;
	elseif (b <= -3e-204)
		tmp = y;
	elseif (b <= 4.9e-26)
		tmp = x;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.8e+21], N[(b * a), $MachinePrecision], If[LessEqual[b, -3e-204], y, If[LessEqual[b, 4.9e-26], x, N[(b * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.8e21 or 4.8999999999999999e-26 < 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. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -7.8e21 < b < -2.9999999999999998e-204

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.9999999999999998e-204 < b < 4.8999999999999999e-26

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 58.3% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;x + y \leq -1 \cdot 10^{-103}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b))) (if (<= (+ x y) -1e-103) (+ 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 ((x + y) <= -1e-103) {
		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 ((x + y) <= (-1d-103)) 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 ((x + y) <= -1e-103) {
		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 (x + y) <= -1e-103:
		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 (Float64(x + y) <= -1e-103)
		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 ((x + y) <= -1e-103)
		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[N[(x + y), $MachinePrecision], -1e-103], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.99999999999999958e-104

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -9.99999999999999958e-104 < (+.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 y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 55.3% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 10^{+28}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 1e+28) (+ x (* (- a 0.5) b)) (+ y (* b a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 1e+28) {
		tmp = x + ((a - 0.5) * b);
	} 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+28) then
        tmp = x + ((a - 0.5d0) * b)
    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+28) {
		tmp = x + ((a - 0.5) * b);
	} else {
		tmp = y + (b * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= 1e+28:
		tmp = x + ((a - 0.5) * b)
	else:
		tmp = y + (b * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= 1e+28)
		tmp = Float64(x + Float64(Float64(a - 0.5) * b));
	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+28)
		tmp = x + ((a - 0.5) * b);
	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+28], N[(x + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 9.99999999999999958e27

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 9.99999999999999958e27 < (+.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 y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 52.2% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+92}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+111}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.06e+92) (* b a) (if (<= a 1.35e+111) (+ x y) (* b a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.06e+92) {
		tmp = b * a;
	} else if (a <= 1.35e+111) {
		tmp = x + y;
	} else {
		tmp = 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 (a <= (-1.06d+92)) then
        tmp = b * a
    else if (a <= 1.35d+111) then
        tmp = x + y
    else
        tmp = 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 (a <= -1.06e+92) {
		tmp = b * a;
	} else if (a <= 1.35e+111) {
		tmp = x + y;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.06e+92:
		tmp = b * a
	elif a <= 1.35e+111:
		tmp = x + y
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.06e+92)
		tmp = Float64(b * a);
	elseif (a <= 1.35e+111)
		tmp = Float64(x + y);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.06e+92)
		tmp = b * a;
	elseif (a <= 1.35e+111)
		tmp = x + y;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.06e+92], N[(b * a), $MachinePrecision], If[LessEqual[a, 1.35e+111], N[(x + y), $MachinePrecision], N[(b * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.05999999999999999e92 or 1.3499999999999999e111 < 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 a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.05999999999999999e92 < a < 1.3499999999999999e111

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 78.4% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(y + x), $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. Taylor expanded in z around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 19: 27.5% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -1.5e+33) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.5e+33) {
		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 <= (-1.5d+33)) 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 <= -1.5e+33) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.5e+33:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.5e+33)
		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 <= -1.5e+33)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.5e+33], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999992e33

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.49999999999999992e33 < x

   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 y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 22.5% 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. Add Preprocessing

3. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
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 2024110 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (+ (+ (+ 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)))