Average Error: 5.7 → 0.1
Time: 15.0s
Precision: binary64
Cost: 448
\[e^{\log a + \log b} \]
↓
\[\frac{1}{\frac{1}{b}} \cdot a \]
(FPCore (a b) :precision binary64 (exp (+ (log a) (log b))))
↓
(FPCore (a b) :precision binary64 (* (/ 1.0 (/ 1.0 b)) a))
double code(double a, double b) {
	return exp((log(a) + log(b)));
}
↓
double code(double a, double b) {
	return (1.0 / (1.0 / b)) * a;
}

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = exp((log(a) + log(b)))
end function
↓
real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (1.0d0 / (1.0d0 / b)) * a
end function

public static double code(double a, double b) {
	return Math.exp((Math.log(a) + Math.log(b)));
}
↓
public static double code(double a, double b) {
	return (1.0 / (1.0 / b)) * a;
}

def code(a, b):
	return math.exp((math.log(a) + math.log(b)))
↓
def code(a, b):
	return (1.0 / (1.0 / b)) * a

function code(a, b)
	return exp(Float64(log(a) + log(b)))
end
↓
function code(a, b)
	return Float64(Float64(1.0 / Float64(1.0 / b)) * a)
end

function tmp = code(a, b)
	tmp = exp((log(a) + log(b)));
end
↓
function tmp = code(a, b)
	tmp = (1.0 / (1.0 / b)) * a;
end

code[a_, b_] := N[Exp[N[(N[Log[a], $MachinePrecision] + N[Log[b], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
↓
code[a_, b_] := N[(N[(1.0 / N[(1.0 / b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]

e^{\log a + \log b}
↓
\frac{1}{\frac{1}{b}} \cdot a

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.7
Target0
Herbie0.1
\[a \cdot b \]

Derivation

  1. Initial program 5.7

    \[e^{\log a + \log b} \]

  2. Applied egg-rr5.4

    \[\leadsto \color{blue}{e^{\log b} \cdot e^{\log a}} \]

  3. Taylor expanded in b around inf 4.7

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

  4. Simplified4.7

    \[\leadsto \color{blue}{\frac{1}{\frac{1}{b}}} \cdot e^{\log a} \]
    Proof

  5. Taylor expanded in a around inf 0.2

    \[\leadsto \frac{1}{\frac{1}{b}} \cdot \color{blue}{{\left(\frac{1}{a}\right)}^{-1}} \]

  6. Simplified0.2

    \[\leadsto \frac{1}{\frac{1}{b}} \cdot \color{blue}{\frac{1}{\frac{1}{a}}} \]
    Proof

  7. Taylor expanded in a around 0 0.1

    \[\leadsto \frac{1}{\frac{1}{b}} \cdot \color{blue}{a} \]

Alternatives

Alternative 1
Error0.1
Cost448
\[b \cdot \frac{1}{\frac{1}{a}} \]

Error

Reproduce

herbie shell --seed 2023010 
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

  (exp (+ (log a) (log b))))