symmetry log of sum of exp

Percentage Accurate: 53.9% → 98.2%

Time: 13.8s

Alternatives: 10

Speedup: 1.5×

• could not determine a ground truth

  1. a = 5.412745222421044e+57
  2. b = 7.278535100164333e+122

Specification

Math

\[\begin{array}{l} \\ \log \left(e^{a} + e^{b}\right) \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (log (+ (exp a) (exp b))))

C

double code(double a, double b) {
	return log((exp(a) + exp(b)));
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = log((exp(a) + exp(b)))
end function

Java

public static double code(double a, double b) {
	return Math.log((Math.exp(a) + Math.exp(b)));
}

Python

def code(a, b):
	return math.log((math.exp(a) + math.exp(b)))

Julia

function code(a, b)
	return log(Float64(exp(a) + exp(b)))
end

MATLAB

function tmp = code(a, b)
	tmp = log((exp(a) + exp(b)));
end

Wolfram

code[a_, b_] := N[Log[N[(N[Exp[a], $MachinePrecision] + N[Exp[b], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Initial Program: 53.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \log \left(e^{a} + e^{b}\right) \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (log (+ (exp a) (exp b))))

C

double code(double a, double b) {
	return log((exp(a) + exp(b)));
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = log((exp(a) + exp(b)))
end function

Java

public static double code(double a, double b) {
	return Math.log((Math.exp(a) + Math.exp(b)));
}

Python

def code(a, b):
	return math.log((math.exp(a) + math.exp(b)))

Julia

function code(a, b)
	return log(Float64(exp(a) + exp(b)))
end

MATLAB

function tmp = code(a, b)
	tmp = log((exp(a) + exp(b)));
end

Wolfram

code[a_, b_] := N[Log[N[(N[Exp[a], $MachinePrecision] + N[Exp[b], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Alternative 1: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \mathsf{log1p}\left(e^{a}\right) + \frac{b}{e^{a} + 1} \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (+ (log1p (exp a)) (/ b (+ (exp a) 1.0))))

C

assert(a < b);
double code(double a, double b) {
	return log1p(exp(a)) + (b / (exp(a) + 1.0));
}

Java

assert a < b;
public static double code(double a, double b) {
	return Math.log1p(Math.exp(a)) + (b / (Math.exp(a) + 1.0));
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return math.log1p(math.exp(a)) + (b / (math.exp(a) + 1.0))

Julia

a, b = sort([a, b])
function code(a, b)
	return Float64(log1p(exp(a)) + Float64(b / Float64(exp(a) + 1.0)))
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[(N[Log[1 + N[Exp[a], $MachinePrecision]], $MachinePrecision] + N[(b / N[(N[Exp[a], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 57.6%

   \[\log \left(e^{a} + e^{b}\right) \]

2. Taylor expanded in b around 0 81.1%

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

   1. log1p-def 81.1%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{a}\right)} + \frac{b}{1 + e^{a}} \]

4. Simplified 81.1%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{a}\right) + \frac{b}{1 + e^{a}}} \]

5. Final simplification 81.1%

   \[\leadsto \mathsf{log1p}\left(e^{a}\right) + \frac{b}{e^{a} + 1} \]

Alternative 2: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \mathsf{log1p}\left(e^{a} + \mathsf{expm1}\left(b\right)\right) \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (log1p (+ (exp a) (expm1 b))))

C

assert(a < b);
double code(double a, double b) {
	return log1p((exp(a) + expm1(b)));
}

Java

assert a < b;
public static double code(double a, double b) {
	return Math.log1p((Math.exp(a) + Math.expm1(b)));
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return math.log1p((math.exp(a) + math.expm1(b)))

Julia

a, b = sort([a, b])
function code(a, b)
	return log1p(Float64(exp(a) + expm1(b)))
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[Log[1 + N[(N[Exp[a], $MachinePrecision] + N[(Exp[b] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 57.6%

   \[\log \left(e^{a} + e^{b}\right) \]
2. Step-by-step derivation

   1. add-sqr-sqrt 56.2%

      \[\leadsto \log \color{blue}{\left(\sqrt{e^{a} + e^{b}} \cdot \sqrt{e^{a} + e^{b}}\right)} \]

   2. log-prod 56.7%

      \[\leadsto \color{blue}{\log \left(\sqrt{e^{a} + e^{b}}\right) + \log \left(\sqrt{e^{a} + e^{b}}\right)} \]

3. Applied egg-rr 56.7%

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

   1. log-prod 56.2%

      \[\leadsto \color{blue}{\log \left(\sqrt{e^{a} + e^{b}} \cdot \sqrt{e^{a} + e^{b}}\right)} \]

   2. rem-square-sqrt 57.6%

      \[\leadsto \log \color{blue}{\left(e^{a} + e^{b}\right)} \]

   3. log1p-expm1 57.6%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(e^{a} + e^{b}\right)\right)\right)} \]

   4. expm1-def 57.6%

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

   5. rem-exp-log 57.6%

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

   6. associate--l+ 57.6%

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

   7. expm1-def 83.7%

      \[\leadsto \mathsf{log1p}\left(e^{a} + \color{blue}{\mathsf{expm1}\left(b\right)}\right) \]

5. Simplified 83.7%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{a} + \mathsf{expm1}\left(b\right)\right)} \]

6. Final simplification 83.7%

   \[\leadsto \mathsf{log1p}\left(e^{a} + \mathsf{expm1}\left(b\right)\right) \]

Alternative 3: 95.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \mathsf{log1p}\left(e^{a} + b\right) \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (log1p (+ (exp a) b)))

C

assert(a < b);
double code(double a, double b) {
	return log1p((exp(a) + b));
}

Java

assert a < b;
public static double code(double a, double b) {
	return Math.log1p((Math.exp(a) + b));
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return math.log1p((math.exp(a) + b))

Julia

a, b = sort([a, b])
function code(a, b)
	return log1p(Float64(exp(a) + b))
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[Log[1 + N[(N[Exp[a], $MachinePrecision] + b), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 57.6%

   \[\log \left(e^{a} + e^{b}\right) \]

2. Taylor expanded in b around 0 54.4%

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

   1. log1p-def 80.4%

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

   2. +-commutative 80.4%

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

4. Applied egg-rr 80.4%

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

5. Final simplification 80.4%

   \[\leadsto \mathsf{log1p}\left(e^{a} + b\right) \]

Alternative 4: 51.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \mathsf{log1p}\left(e^{a}\right) \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (log1p (exp a)))

C

assert(a < b);
double code(double a, double b) {
	return log1p(exp(a));
}

Java

assert a < b;
public static double code(double a, double b) {
	return Math.log1p(Math.exp(a));
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return math.log1p(math.exp(a))

Julia

a, b = sort([a, b])
function code(a, b)
	return log1p(exp(a))
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[Log[1 + N[Exp[a], $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 57.6%

   \[\log \left(e^{a} + e^{b}\right) \]

2. Taylor expanded in b around 0 54.7%

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

   1. log1p-def 54.7%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{a}\right)} \]

4. Simplified 54.7%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{a}\right)} \]

5. Final simplification 54.7%

   \[\leadsto \mathsf{log1p}\left(e^{a}\right) \]

Alternative 5: 49.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \log \left(2 + \left(a + \left(b + 0.5 \cdot \left(a \cdot a\right)\right)\right)\right) \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (log (+ 2.0 (+ a (+ b (* 0.5 (* a a)))))))

C

assert(a < b);
double code(double a, double b) {
	return log((2.0 + (a + (b + (0.5 * (a * a))))));
}

Fortran

NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = log((2.0d0 + (a + (b + (0.5d0 * (a * a))))))
end function

Java

assert a < b;
public static double code(double a, double b) {
	return Math.log((2.0 + (a + (b + (0.5 * (a * a))))));
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return math.log((2.0 + (a + (b + (0.5 * (a * a))))))

Julia

a, b = sort([a, b])
function code(a, b)
	return log(Float64(2.0 + Float64(a + Float64(b + Float64(0.5 * Float64(a * a))))))
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp = code(a, b)
	tmp = log((2.0 + (a + (b + (0.5 * (a * a))))));
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[Log[N[(2.0 + N[(a + N[(b + N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 57.6%

   \[\log \left(e^{a} + e^{b}\right) \]

2. Taylor expanded in b around 0 54.4%

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

3. Taylor expanded in a around 0 53.2%

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

   1. +-commutative 53.2%

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

   2. unpow2 53.2%

      \[\leadsto \log \left(2 + \left(a + \left(0.5 \cdot \color{blue}{\left(a \cdot a\right)} + b\right)\right)\right) \]

5. Simplified 53.2%

   \[\leadsto \log \color{blue}{\left(2 + \left(a + \left(0.5 \cdot \left(a \cdot a\right) + b\right)\right)\right)} \]

6. Final simplification 53.2%

   \[\leadsto \log \left(2 + \left(a + \left(b + 0.5 \cdot \left(a \cdot a\right)\right)\right)\right) \]

Alternative 6: 49.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \log \left(2 + \left(a + 0.5 \cdot \left(a \cdot a\right)\right)\right) \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (log (+ 2.0 (+ a (* 0.5 (* a a))))))

C

assert(a < b);
double code(double a, double b) {
	return log((2.0 + (a + (0.5 * (a * a)))));
}

Fortran

NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = log((2.0d0 + (a + (0.5d0 * (a * a)))))
end function

Java

assert a < b;
public static double code(double a, double b) {
	return Math.log((2.0 + (a + (0.5 * (a * a)))));
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return math.log((2.0 + (a + (0.5 * (a * a)))))

Julia

a, b = sort([a, b])
function code(a, b)
	return log(Float64(2.0 + Float64(a + Float64(0.5 * Float64(a * a)))))
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp = code(a, b)
	tmp = log((2.0 + (a + (0.5 * (a * a)))));
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[Log[N[(2.0 + N[(a + N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 57.6%

   \[\log \left(e^{a} + e^{b}\right) \]

2. Taylor expanded in b around 0 54.4%

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

3. Taylor expanded in a around 0 53.2%

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

   1. +-commutative 53.2%

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

   2. unpow2 53.2%

      \[\leadsto \log \left(2 + \left(a + \left(0.5 \cdot \color{blue}{\left(a \cdot a\right)} + b\right)\right)\right) \]

5. Simplified 53.2%

   \[\leadsto \log \color{blue}{\left(2 + \left(a + \left(0.5 \cdot \left(a \cdot a\right) + b\right)\right)\right)} \]

6. Taylor expanded in b around 0 53.6%

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

   1. unpow2 53.6%

      \[\leadsto \log \left(2 + \left(a + 0.5 \cdot \color{blue}{\left(a \cdot a\right)}\right)\right) \]

8. Simplified 53.6%

   \[\leadsto \color{blue}{\log \left(2 + \left(a + 0.5 \cdot \left(a \cdot a\right)\right)\right)} \]

9. Final simplification 53.6%

   \[\leadsto \log \left(2 + \left(a + 0.5 \cdot \left(a \cdot a\right)\right)\right) \]

Alternative 7: 49.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ b \cdot 0.5 + \log 2 \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (+ (* b 0.5) (log 2.0)))

C

assert(a < b);
double code(double a, double b) {
	return (b * 0.5) + log(2.0);
}

Fortran

NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (b * 0.5d0) + log(2.0d0)
end function

Java

assert a < b;
public static double code(double a, double b) {
	return (b * 0.5) + Math.log(2.0);
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return (b * 0.5) + math.log(2.0)

Julia

a, b = sort([a, b])
function code(a, b)
	return Float64(Float64(b * 0.5) + log(2.0))
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp = code(a, b)
	tmp = (b * 0.5) + log(2.0);
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[(N[(b * 0.5), $MachinePrecision] + N[Log[2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 57.6%

   \[\log \left(e^{a} + e^{b}\right) \]

2. Taylor expanded in a around 0 54.4%

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

   1. log1p-def 54.4%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{b}\right)} \]

4. Simplified 54.4%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{b}\right)} \]

5. Taylor expanded in b around 0 53.5%

   \[\leadsto \color{blue}{\log 2 + 0.5 \cdot b} \]
6. Step-by-step derivation

   1. +-commutative 53.5%

      \[\leadsto \color{blue}{0.5 \cdot b + \log 2} \]

7. Simplified 53.5%

   \[\leadsto \color{blue}{0.5 \cdot b + \log 2} \]

8. Final simplification 53.5%

   \[\leadsto b \cdot 0.5 + \log 2 \]

Alternative 8: 49.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \log \left(b + 2\right) \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (log (+ b 2.0)))

C

assert(a < b);
double code(double a, double b) {
	return log((b + 2.0));
}

Fortran

NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = log((b + 2.0d0))
end function

Java

assert a < b;
public static double code(double a, double b) {
	return Math.log((b + 2.0));
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return math.log((b + 2.0))

Julia

a, b = sort([a, b])
function code(a, b)
	return log(Float64(b + 2.0))
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp = code(a, b)
	tmp = log((b + 2.0));
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[Log[N[(b + 2.0), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 57.6%

   \[\log \left(e^{a} + e^{b}\right) \]

2. Taylor expanded in b around 0 54.4%

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

3. Taylor expanded in a around 0 52.9%

   \[\leadsto \color{blue}{\log \left(2 + b\right)} \]

4. Final simplification 52.9%

   \[\leadsto \log \left(b + 2\right) \]

Alternative 9: 49.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \log 2 \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (log 2.0))

C

assert(a < b);
double code(double a, double b) {
	return log(2.0);
}

Fortran

NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = log(2.0d0)
end function

Java

assert a < b;
public static double code(double a, double b) {
	return Math.log(2.0);
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return math.log(2.0)

Julia

a, b = sort([a, b])
function code(a, b)
	return log(2.0)
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp = code(a, b)
	tmp = log(2.0);
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[Log[2.0], $MachinePrecision]

Derivation

1. Initial program 57.6%

   \[\log \left(e^{a} + e^{b}\right) \]

2. Taylor expanded in b around 0 54.7%

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

   1. log1p-def 54.7%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{a}\right)} \]

4. Simplified 54.7%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{a}\right)} \]

5. Taylor expanded in a around 0 53.4%

   \[\leadsto \color{blue}{\log 2} \]

6. Final simplification 53.4%

   \[\leadsto \log 2 \]

Alternative 10: 2.6% accurate, 101.0× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ a \cdot 0.5 \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (* a 0.5))

C

assert(a < b);
double code(double a, double b) {
	return a * 0.5;
}

Fortran

NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a * 0.5d0
end function

Java

assert a < b;
public static double code(double a, double b) {
	return a * 0.5;
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return a * 0.5

Julia

a, b = sort([a, b])
function code(a, b)
	return Float64(a * 0.5)
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp = code(a, b)
	tmp = a * 0.5;
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[(a * 0.5), $MachinePrecision]

Derivation

1. Initial program 57.6%

   \[\log \left(e^{a} + e^{b}\right) \]

2. Taylor expanded in b around 0 54.7%

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

   1. log1p-def 54.7%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{a}\right)} \]

4. Simplified 54.7%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{a}\right)} \]

5. Taylor expanded in a around 0 53.3%

   \[\leadsto \color{blue}{\log 2 + 0.5 \cdot a} \]
6. Step-by-step derivation

   1. *-commutative 53.3%

      \[\leadsto \log 2 + \color{blue}{a \cdot 0.5} \]

7. Simplified 53.3%

   \[\leadsto \color{blue}{\log 2 + a \cdot 0.5} \]

8. Taylor expanded in a around inf 6.2%

   \[\leadsto \color{blue}{0.5 \cdot a} \]
9. Step-by-step derivation

   1. *-commutative 6.2%

      \[\leadsto \color{blue}{a \cdot 0.5} \]

10. Simplified 6.2%

    \[\leadsto \color{blue}{a \cdot 0.5} \]

11. Final simplification 6.2%

    \[\leadsto a \cdot 0.5 \]

Reproduce

herbie shell --seed 2023271 
(FPCore (a b)
  :name "symmetry log of sum of exp"
  :precision binary64
  (log (+ (exp a) (exp b))))