symmetry log of sum of exp

Percentage Accurate: 52.7% → 98.3%

Time: 19.0s

Alternatives: 11

Speedup: 1.5×

• could not determine a ground truth

  1. a = 5.075099417926167e+23
  2. b = -4.4105852844559444e+169

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: 52.7% 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: 98.3% 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 57.5%

   \[\log \left(e^{a} + e^{b}\right) \]
2. Add Preprocessing

3. Taylor expanded in b around 0 73.6%

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

   1. log1p-define 73.6%

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

5. Simplified 73.6%

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

6. Final simplification 73.6%

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

Alternative 2: 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 57.5%

   \[\log \left(e^{a} + e^{b}\right) \]
2. Add Preprocessing

3. Taylor expanded in b around 0 54.7%

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

   1. associate-+r+ 54.7%

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

   2. +-commutative 54.7%

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

5. Simplified 54.7%

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

6. Taylor expanded in a around inf 54.7%

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

   1. log1p-define 72.4%

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

8. Simplified 72.4%

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

9. Final simplification 72.4%

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

Alternative 3: 49.9% 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 57.5%

   \[\log \left(e^{a} + e^{b}\right) \]
2. Add Preprocessing

3. Taylor expanded in b around 0 54.8%

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

   1. log1p-define 54.8%

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

5. Simplified 54.8%

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

6. Final simplification 54.8%

   \[\leadsto \mathsf{log1p}\left(e^{a}\right) \]
7. Add Preprocessing

Alternative 4: 48.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \log \left(2 + \left(b + a \cdot \left(1 + a \cdot 0.5\right)\right)\right) \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (log (+ 2.0 (+ b (* a (+ 1.0 (* a 0.5)))))))

C

assert(a < b);
double code(double a, double b) {
	return log((2.0 + (b + (a * (1.0 + (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 = log((2.0d0 + (b + (a * (1.0d0 + (a * 0.5d0))))))
end function

Java

assert a < b;
public static double code(double a, double b) {
	return Math.log((2.0 + (b + (a * (1.0 + (a * 0.5))))));
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return math.log((2.0 + (b + (a * (1.0 + (a * 0.5))))))

Julia

a, b = sort([a, b])
function code(a, b)
	return log(Float64(2.0 + Float64(b + Float64(a * Float64(1.0 + Float64(a * 0.5))))))
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp = code(a, b)
	tmp = log((2.0 + (b + (a * (1.0 + (a * 0.5))))));
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[(b + N[(a * N[(1.0 + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 57.5%

   \[\log \left(e^{a} + e^{b}\right) \]
2. Add Preprocessing

3. Taylor expanded in b around 0 54.7%

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

   1. associate-+r+ 54.7%

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

   2. +-commutative 54.7%

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

5. Simplified 54.7%

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

6. Taylor expanded in a around 0 53.7%

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

   1. +-commutative 53.7%

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

   2. *-commutative 53.7%

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

8. Simplified 53.7%

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

9. Final simplification 53.7%

   \[\leadsto \log \left(2 + \left(b + a \cdot \left(1 + a \cdot 0.5\right)\right)\right) \]
10. Add Preprocessing

Alternative 5: 48.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} [a, b] = \mathsf{sort}([a, b])\\ \\ \log 2 + b \cdot \left(0.5 + b \cdot 0.125\right) \end{array} \]

FPCore

NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (a b) :precision binary64 (+ (log 2.0) (* b (+ 0.5 (* b 0.125)))))

C

assert(a < b);
double code(double a, double b) {
	return log(2.0) + (b * (0.5 + (b * 0.125)));
}

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) + (b * (0.5d0 + (b * 0.125d0)))
end function

Java

assert a < b;
public static double code(double a, double b) {
	return Math.log(2.0) + (b * (0.5 + (b * 0.125)));
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return math.log(2.0) + (b * (0.5 + (b * 0.125)))

Julia

a, b = sort([a, b])
function code(a, b)
	return Float64(log(2.0) + Float64(b * Float64(0.5 + Float64(b * 0.125))))
end

MATLAB

a, b = num2cell(sort([a, b])){:}
function tmp = code(a, b)
	tmp = log(2.0) + (b * (0.5 + (b * 0.125)));
end

Wolfram

NOTE: a and b should be sorted in increasing order before calling this function.
code[a_, b_] := N[(N[Log[2.0], $MachinePrecision] + N[(b * N[(0.5 + N[(b * 0.125), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 57.5%

   \[\log \left(e^{a} + e^{b}\right) \]
2. Add Preprocessing

3. Taylor expanded in a around 0 55.0%

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

   1. log1p-define 55.0%

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

5. Simplified 55.0%

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

6. Taylor expanded in b around 0 53.7%

   \[\leadsto \color{blue}{\log 2 + b \cdot \left(0.5 + 0.125 \cdot b\right)} \]
7. Step-by-step derivation

   1. *-commutative 53.7%

      \[\leadsto \log 2 + b \cdot \left(0.5 + \color{blue}{b \cdot 0.125}\right) \]

8. Simplified 53.7%

   \[\leadsto \color{blue}{\log 2 + b \cdot \left(0.5 + b \cdot 0.125\right)} \]

9. Final simplification 53.7%

   \[\leadsto \log 2 + b \cdot \left(0.5 + b \cdot 0.125\right) \]
10. Add Preprocessing

Alternative 6: 48.6% accurate, 2.9× speedup

Math

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

FPCore

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

C

assert(a < b);
double code(double a, double b) {
	return log(2.0) + (b * 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 = log(2.0d0) + (b * 0.5d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.5%

   \[\log \left(e^{a} + e^{b}\right) \]
2. Add Preprocessing

3. Taylor expanded in a around 0 55.0%

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

   1. log1p-define 55.0%

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

5. Simplified 55.0%

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

6. Taylor expanded in b around 0 53.5%

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

   1. +-commutative 53.5%

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

8. Simplified 53.5%

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

9. Final simplification 53.5%

   \[\leadsto \log 2 + b \cdot 0.5 \]
10. Add Preprocessing

Alternative 7: 48.3% 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 57.5%

   \[\log \left(e^{a} + e^{b}\right) \]
2. Add Preprocessing

3. Taylor expanded in b around 0 54.7%

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

   1. associate-+r+ 54.7%

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

   2. +-commutative 54.7%

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

5. Simplified 54.7%

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

6. Taylor expanded in a around 0 52.8%

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

7. Final simplification 52.8%

   \[\leadsto \log \left(b + 2\right) \]
8. Add Preprocessing

Alternative 8: 47.9% 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 57.5%

   \[\log \left(e^{a} + e^{b}\right) \]
2. Add Preprocessing

3. Taylor expanded in a around 0 55.0%

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

   1. log1p-define 55.0%

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

5. Simplified 55.0%

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

6. Taylor expanded in b around 0 53.2%

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

7. Final simplification 53.2%

   \[\leadsto \log 2 \]
8. Add Preprocessing

Alternative 9: 2.8% accurate, 33.7× speedup

Math

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

FPCore

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

C

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

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 + ((a / b) * (-2.0d0))) / b
end function

Java

assert a < b;
public static double code(double a, double b) {
	return (a + ((a / b) * -2.0)) / b;
}

Python

[a, b] = sort([a, b])
def code(a, b):
	return (a + ((a / b) * -2.0)) / b

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.5%

   \[\log \left(e^{a} + e^{b}\right) \]
2. Add Preprocessing

3. Taylor expanded in b around 0 54.7%

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

   1. associate-+r+ 54.7%

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

   2. +-commutative 54.7%

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

5. Simplified 54.7%

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

6. Taylor expanded in a around 0 53.3%

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

7. Taylor expanded in a around inf 4.0%

   \[\leadsto \color{blue}{\frac{a}{2 + b}} \]

8. Taylor expanded in b around inf 3.3%

   \[\leadsto \color{blue}{\frac{a + -2 \cdot \frac{a}{b}}{b}} \]
9. Step-by-step derivation

   1. *-commutative 3.3%

      \[\leadsto \frac{a + \color{blue}{\frac{a}{b} \cdot -2}}{b} \]

10. Simplified 3.3%

    \[\leadsto \color{blue}{\frac{a + \frac{a}{b} \cdot -2}{b}} \]

11. Final simplification 3.3%

    \[\leadsto \frac{a + \frac{a}{b} \cdot -2}{b} \]
12. Add Preprocessing

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 57.5%

   \[\log \left(e^{a} + e^{b}\right) \]
2. Add Preprocessing

3. Taylor expanded in b around 0 54.7%

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

   1. associate-+r+ 54.7%

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

   2. +-commutative 54.7%

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

5. Simplified 54.7%

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

6. Taylor expanded in a around 0 53.3%

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

7. Taylor expanded in a around inf 4.0%

   \[\leadsto \color{blue}{\frac{a}{2 + b}} \]

8. Taylor expanded in b around 0 7.5%

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

   1. *-commutative 7.5%

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

10. Simplified 7.5%

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

11. Final simplification 7.5%

    \[\leadsto a \cdot 0.5 \]
12. Add Preprocessing

Alternative 11: 2.6% accurate, 101.0× speedup

Math

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

FPCore

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

C

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

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 / b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.5%

   \[\log \left(e^{a} + e^{b}\right) \]
2. Add Preprocessing

3. Taylor expanded in b around 0 54.7%

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

   1. associate-+r+ 54.7%

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

   2. +-commutative 54.7%

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

5. Simplified 54.7%

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

6. Taylor expanded in a around 0 53.3%

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

7. Taylor expanded in a around inf 4.0%

   \[\leadsto \color{blue}{\frac{a}{2 + b}} \]

8. Taylor expanded in b around inf 3.7%

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

9. Final simplification 3.7%

   \[\leadsto \frac{a}{b} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (a b)
  :name "symmetry log of sum of exp"
  :precision binary64
  (log (+ (exp a) (exp b))))