Average Error: 3.7 → 2.7
Time: 15.0s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\sqrt[3]{\log \left(e^{d + \left(b + \left(a + c\right)\right)}\right) \cdot \left(\left(d + \left(\left(b + c\right) + a\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right)} \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\sqrt[3]{\log \left(e^{d + \left(b + \left(a + c\right)\right)}\right) \cdot \left(\left(d + \left(\left(b + c\right) + a\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right)} \cdot 2
double f(double a, double b, double c, double d) {
        double r3256879 = a;
        double r3256880 = b;
        double r3256881 = c;
        double r3256882 = d;
        double r3256883 = r3256881 + r3256882;
        double r3256884 = r3256880 + r3256883;
        double r3256885 = r3256879 + r3256884;
        double r3256886 = 2.0;
        double r3256887 = r3256885 * r3256886;
        return r3256887;
}
↓
double f(double a, double b, double c, double d) {
        double r3256888 = d;
        double r3256889 = b;
        double r3256890 = a;
        double r3256891 = c;
        double r3256892 = r3256890 + r3256891;
        double r3256893 = r3256889 + r3256892;
        double r3256894 = r3256888 + r3256893;
        double r3256895 = exp(r3256894);
        double r3256896 = log(r3256895);
        double r3256897 = r3256889 + r3256891;
        double r3256898 = r3256897 + r3256890;
        double r3256899 = r3256888 + r3256898;
        double r3256900 = r3256897 + r3256888;
        double r3256901 = r3256890 + r3256900;
        double r3256902 = r3256899 * r3256901;
        double r3256903 = r3256896 * r3256902;
        double r3256904 = cbrt(r3256903);
        double r3256905 = 2.0;
        double r3256906 = r3256904 * r3256905;
        return r3256906;
}

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
Herbie2.7
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.7

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

  3. Applied 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 associate-+r+2.7

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

  9. Applied add-log-exp2.7

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

  10. Applied add-log-exp2.7

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

  11. Applied sum-log2.7

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

  12. Applied add-log-exp2.7

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

  13. Applied sum-log2.3

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

  14. Simplified2.7

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

  15. Final simplification2.7

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

Reproduce

herbie shell --seed 2019143 
(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))