Average Error: 3.6 → 0
Time: 7.0s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(c + b\right) + \left(d + a\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(c + b\right) + \left(d + a\right)\right)
double f(double a, double b, double c, double d) {
        double r2394746 = a;
        double r2394747 = b;
        double r2394748 = c;
        double r2394749 = d;
        double r2394750 = r2394748 + r2394749;
        double r2394751 = r2394747 + r2394750;
        double r2394752 = r2394746 + r2394751;
        double r2394753 = 2.0;
        double r2394754 = r2394752 * r2394753;
        return r2394754;
}
↓
double f(double a, double b, double c, double d) {
        double r2394755 = 2.0;
        double r2394756 = c;
        double r2394757 = b;
        double r2394758 = r2394756 + r2394757;
        double r2394759 = d;
        double r2394760 = a;
        double r2394761 = r2394759 + r2394760;
        double r2394762 = r2394758 + r2394761;
        double r2394763 = r2394755 * r2394762;
        return r2394763;
}

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

Original3.6
Target3.8
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.6

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

  3. Applied add-log-exp3.6

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

  4. Applied add-log-exp3.6

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

  5. Applied sum-log3.6

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

  6. Applied add-log-exp3.6

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

  7. Applied sum-log3.7

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

  8. Simplified3.0

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

  10. Applied *-un-lft-identity3.0

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

  11. Applied log-prod3.0

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

  12. Simplified3.0

    \[\leadsto \left(\color{blue}{0} + \log \left(e^{c + \left(a + \left(b + d\right)\right)}\right)\right) \cdot 2\]

  13. Simplified0

    \[\leadsto \left(0 + \color{blue}{\left(\left(c + b\right) + \left(a + d\right)\right)}\right) \cdot 2\]

  14. Final simplification0

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

Reproduce

herbie shell --seed 2019130 
(FPCore (a b c d)
  :name "Expression, p6"
  :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))