Average Error: 3.6 → 2.9
Time: 15.7s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\sqrt[3]{\left(\left(\left(d + \left(c + b\right)\right) + a\right) \cdot \log \left(e^{d + \left(\left(c + a\right) + b\right)}\right)\right) \cdot \frac{a \cdot a - \left(d + \left(c + b\right)\right) \cdot \left(d + \left(c + b\right)\right)}{a - \left(d + \left(c + b\right)\right)}} \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\sqrt[3]{\left(\left(\left(d + \left(c + b\right)\right) + a\right) \cdot \log \left(e^{d + \left(\left(c + a\right) + b\right)}\right)\right) \cdot \frac{a \cdot a - \left(d + \left(c + b\right)\right) \cdot \left(d + \left(c + b\right)\right)}{a - \left(d + \left(c + b\right)\right)}} \cdot 2
double f(double a, double b, double c, double d) {
        double r3044826 = a;
        double r3044827 = b;
        double r3044828 = c;
        double r3044829 = d;
        double r3044830 = r3044828 + r3044829;
        double r3044831 = r3044827 + r3044830;
        double r3044832 = r3044826 + r3044831;
        double r3044833 = 2.0;
        double r3044834 = r3044832 * r3044833;
        return r3044834;
}
↓
double f(double a, double b, double c, double d) {
        double r3044835 = d;
        double r3044836 = c;
        double r3044837 = b;
        double r3044838 = r3044836 + r3044837;
        double r3044839 = r3044835 + r3044838;
        double r3044840 = a;
        double r3044841 = r3044839 + r3044840;
        double r3044842 = r3044836 + r3044840;
        double r3044843 = r3044842 + r3044837;
        double r3044844 = r3044835 + r3044843;
        double r3044845 = exp(r3044844);
        double r3044846 = log(r3044845);
        double r3044847 = r3044841 * r3044846;
        double r3044848 = r3044840 * r3044840;
        double r3044849 = r3044839 * r3044839;
        double r3044850 = r3044848 - r3044849;
        double r3044851 = r3044840 - r3044839;
        double r3044852 = r3044850 / r3044851;
        double r3044853 = r3044847 * r3044852;
        double r3044854 = cbrt(r3044853);
        double r3044855 = 2.0;
        double r3044856 = r3044854 * r3044855;
        return r3044856;
}

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
Herbie2.9
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.6

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

  3. Applied associate-+r+2.8

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

  5. Applied add-cbrt-cube2.9

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)}} \cdot 2\]
  6. Using strategy rm

  7. Applied add-log-exp2.9

    \[\leadsto \sqrt[3]{\left(\left(a + \left(\left(b + c\right) + \color{blue}{\log \left(e^{d}\right)}\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]

  8. Applied add-log-exp2.9

    \[\leadsto \sqrt[3]{\left(\left(a + \left(\color{blue}{\log \left(e^{b + c}\right)} + \log \left(e^{d}\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]

  9. Applied sum-log2.7

    \[\leadsto \sqrt[3]{\left(\left(a + \color{blue}{\log \left(e^{b + c} \cdot e^{d}\right)}\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]

  10. Applied add-log-exp2.7

    \[\leadsto \sqrt[3]{\left(\left(\color{blue}{\log \left(e^{a}\right)} + \log \left(e^{b + c} \cdot e^{d}\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]

  11. Applied sum-log2.6

    \[\leadsto \sqrt[3]{\left(\color{blue}{\log \left(e^{a} \cdot \left(e^{b + c} \cdot e^{d}\right)\right)} \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]

  12. Simplified2.7

    \[\leadsto \sqrt[3]{\left(\log \color{blue}{\left(e^{\left(b + \left(c + a\right)\right) + d}\right)} \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]
  13. Using strategy rm

  14. Applied flip-+2.9

    \[\leadsto \sqrt[3]{\left(\log \left(e^{\left(b + \left(c + a\right)\right) + d}\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \color{blue}{\frac{a \cdot a - \left(\left(b + c\right) + d\right) \cdot \left(\left(b + c\right) + d\right)}{a - \left(\left(b + c\right) + d\right)}}} \cdot 2\]

  15. Final simplification2.9

    \[\leadsto \sqrt[3]{\left(\left(\left(d + \left(c + b\right)\right) + a\right) \cdot \log \left(e^{d + \left(\left(c + a\right) + b\right)}\right)\right) \cdot \frac{a \cdot a - \left(d + \left(c + b\right)\right) \cdot \left(d + \left(c + b\right)\right)}{a - \left(d + \left(c + b\right)\right)}} \cdot 2\]

Reproduce

herbie shell --seed 2019134 
(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))