Average Error: 5.7 → 0
Time: 1.4s
Precision: binary64
Cost: 192
\[e^{\log a + \log b}\]
↓
\[a \cdot b\]
e^{\log a + \log b}
↓
a \cdot b
(FPCore (a b) :precision binary64 (exp (+ (log a) (log b))))
↓
(FPCore (a b) :precision binary64 (* a b))
double code(double a, double b) {
	return exp(log(a) + log(b));
}
↓
double code(double a, double b) {
	return a * b;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Alternatives

Alternative 1
Error5.7
Cost19392
\[e^{\log a + \log b}\]
Alternative 2
Error60.5
Cost64
\[1\]
Alternative 3
Error53.6
Cost64
\[0\]
Alternative 4
Error62.8
Cost64
\[-1\]

Error

Derivation

  1. Initial program 5.7

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

  2. Simplified0

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

  3. Simplified0

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

  4. Final simplification0

    \[\leadsto a \cdot b\]

Reproduce

herbie shell --seed 2021022 
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

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