Average Error: 3.7 → 0
Time: 6.6s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(a + d\right) + \left(b + c\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(a + d\right) + \left(b + c\right)\right)
double f(double a, double b, double c, double d) {
        double r118589 = a;
        double r118590 = b;
        double r118591 = c;
        double r118592 = d;
        double r118593 = r118591 + r118592;
        double r118594 = r118590 + r118593;
        double r118595 = r118589 + r118594;
        double r118596 = 2.0;
        double r118597 = r118595 * r118596;
        return r118597;
}
↓
double f(double a, double b, double c, double d) {
        double r118598 = 2.0;
        double r118599 = a;
        double r118600 = d;
        double r118601 = r118599 + r118600;
        double r118602 = b;
        double r118603 = c;
        double r118604 = r118602 + r118603;
        double r118605 = r118601 + r118604;
        double r118606 = r118598 * r118605;
        return r118606;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.7
Target3.8
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.7

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

  3. Applied add-log-exp3.7

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

  4. Applied add-log-exp3.7

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

  5. Applied sum-log3.7

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

  6. Applied add-log-exp3.7

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

  7. Applied sum-log2.8

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

  8. Simplified2.8

    \[\leadsto \left(a + \log \color{blue}{\left(e^{d + \left(b + c\right)}\right)}\right) \cdot 2\]
  9. Using strategy rm

  10. Applied exp-sum2.8

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

  11. Applied log-prod2.8

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

  12. Applied associate-+r+0.5

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

  13. Simplified0.5

    \[\leadsto \left(\color{blue}{\left(a + d\right)} + \log \left(e^{b + c}\right)\right) \cdot 2\]
  14. Using strategy rm

  15. Applied *-un-lft-identity0.5

    \[\leadsto \left(\left(a + d\right) + \log \left(e^{\color{blue}{1 \cdot \left(b + c\right)}}\right)\right) \cdot 2\]

  16. Applied exp-prod0.7

    \[\leadsto \left(\left(a + d\right) + \log \color{blue}{\left({\left(e^{1}\right)}^{\left(b + c\right)}\right)}\right) \cdot 2\]

  17. Applied log-pow0

    \[\leadsto \left(\left(a + d\right) + \color{blue}{\left(b + c\right) \cdot \log \left(e^{1}\right)}\right) \cdot 2\]

  18. Simplified0

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

  19. Final simplification0

    \[\leadsto 2 \cdot \left(\left(a + d\right) + \left(b + c\right)\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (a b c d)
  :name "Expression, p6"
  :precision binary64
  :pre (and (<= -14 a -13) (<= -3 b -2) (<= 3 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2) (* (+ c d) 2))

  (* (+ a (+ b (+ c d))) 2))