Average Error: 3.6 → 2.7
Time: 1.5m
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\sqrt[3]{\left(\left(\left(\left(b + c\right) + d\right) + a\right) \cdot \log \left(e^{b + \left(a + \left(d + c\right)\right)}\right)\right) \cdot \left(\left(a + \left(b + c\right)\right) + d\right)} \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\sqrt[3]{\left(\left(\left(\left(b + c\right) + d\right) + a\right) \cdot \log \left(e^{b + \left(a + \left(d + c\right)\right)}\right)\right) \cdot \left(\left(a + \left(b + c\right)\right) + d\right)} \cdot 2
double f(double a, double b, double c, double d) {
        double r27292719 = a;
        double r27292720 = b;
        double r27292721 = c;
        double r27292722 = d;
        double r27292723 = r27292721 + r27292722;
        double r27292724 = r27292720 + r27292723;
        double r27292725 = r27292719 + r27292724;
        double r27292726 = 2.0;
        double r27292727 = r27292725 * r27292726;
        return r27292727;
}
↓
double f(double a, double b, double c, double d) {
        double r27292728 = b;
        double r27292729 = c;
        double r27292730 = r27292728 + r27292729;
        double r27292731 = d;
        double r27292732 = r27292730 + r27292731;
        double r27292733 = a;
        double r27292734 = r27292732 + r27292733;
        double r27292735 = r27292731 + r27292729;
        double r27292736 = r27292733 + r27292735;
        double r27292737 = r27292728 + r27292736;
        double r27292738 = exp(r27292737);
        double r27292739 = log(r27292738);
        double r27292740 = r27292734 * r27292739;
        double r27292741 = r27292733 + r27292730;
        double r27292742 = r27292741 + r27292731;
        double r27292743 = r27292740 * r27292742;
        double r27292744 = cbrt(r27292743);
        double r27292745 = 2.0;
        double r27292746 = r27292744 * r27292745;
        return r27292746;
}

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

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 associate-+r+2.7

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

  9. Applied add-log-exp2.7

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

  10. Applied add-log-exp2.7

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

  11. Applied sum-log2.6

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

  12. Applied add-log-exp2.6

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

  13. Applied sum-log2.3

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

  14. Simplified2.7

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

  15. Final simplification2.7

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

Reproduce

herbie shell --seed 2019125 
(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))