Average Error: 3.6 → 0
Time: 6.2s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(\left(a + d\right) + c\right) + b\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(\left(a + d\right) + c\right) + b\right)
double f(double a, double b, double c, double d) {
        double r2714038 = a;
        double r2714039 = b;
        double r2714040 = c;
        double r2714041 = d;
        double r2714042 = r2714040 + r2714041;
        double r2714043 = r2714039 + r2714042;
        double r2714044 = r2714038 + r2714043;
        double r2714045 = 2.0;
        double r2714046 = r2714044 * r2714045;
        return r2714046;
}
↓
double f(double a, double b, double c, double d) {
        double r2714047 = 2.0;
        double r2714048 = a;
        double r2714049 = d;
        double r2714050 = r2714048 + r2714049;
        double r2714051 = c;
        double r2714052 = r2714050 + r2714051;
        double r2714053 = b;
        double r2714054 = r2714052 + r2714053;
        double r2714055 = r2714047 * r2714054;
        return r2714055;
}

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. Simplified0.9

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

  10. Applied rem-log-exp0.0

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

  12. Applied associate-+l+0

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

  13. Final simplification0

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

Reproduce

herbie shell --seed 2019138 
(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))