Average Error: 0.0 → 0.0
Time: 1.6s
Precision: binary64
\[5 \leq a \land a \leq 10 \land 0 \leq b \land b \leq 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot \left(a + b\right) + \log \left({\left(e^{b}\right)}^{\left(a + b\right)}\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
a \cdot \left(a + b\right) + \log \left({\left(e^{b}\right)}^{\left(a + b\right)}\right)
(FPCore (a b) :precision binary64 (* (+ a b) (+ a b)))
↓
(FPCore (a b)
 :precision binary64
 (+ (* a (+ a b)) (log (pow (exp b) (+ a b)))))
double code(double a, double b) {
	return ((double) (((double) (a + b)) * ((double) (a + b))));
}
↓
double code(double a, double b) {
	return ((double) (((double) (a * ((double) (a + b)))) + ((double) log(((double) pow(((double) exp(b)), ((double) (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

Original0.0
Target0.0
Herbie0.0
\[\left(\left(b \cdot a + b \cdot b\right) + b \cdot a\right) + a \cdot a\]

Derivation

  1. Initial program Error: 0.0 bits

    \[\left(a + b\right) \cdot \left(a + b\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-inError: 0.0 bits

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

  4. SimplifiedError: 0.0 bits

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

  5. SimplifiedError: 0.0 bits

    \[\leadsto a \cdot \left(a + b\right) + \color{blue}{b \cdot \left(a + b\right)}\]
  6. Using strategy rm

  7. Applied add-log-expError: 0.0 bits

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

  8. SimplifiedError: 0.0 bits

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

  9. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020203 
(FPCore (a b)
  :name "Expression 4, p15"
  :precision binary64
  :pre (and (<= 5.0 a 10.0) (<= 0.0 b 0.001))

  :herbie-target
  (+ (+ (+ (* b a) (* b b)) (* b a)) (* a a))

  (* (+ a b) (+ a b)))