Average Error: 0.4 → 0.3
Time: 8.9s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\log \left(e^{d}\right) + \left(\left(b + a\right) + \left(e + c\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\log \left(e^{d}\right) + \left(\left(b + a\right) + \left(e + c\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r69581 = e;
        double r69582 = d;
        double r69583 = r69581 + r69582;
        double r69584 = c;
        double r69585 = r69583 + r69584;
        double r69586 = b;
        double r69587 = r69585 + r69586;
        double r69588 = a;
        double r69589 = r69587 + r69588;
        return r69589;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r69590 = d;
        double r69591 = exp(r69590);
        double r69592 = log(r69591);
        double r69593 = b;
        double r69594 = a;
        double r69595 = r69593 + r69594;
        double r69596 = e;
        double r69597 = c;
        double r69598 = r69596 + r69597;
        double r69599 = r69595 + r69598;
        double r69600 = r69592 + r69599;
        return r69600;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.3
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

Derivation

  1. Initial program 0.4

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

  3. Applied associate-+l+0.3

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

  5. Applied add-log-exp0.3

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

  6. Applied add-log-exp0.3

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

  7. Applied add-log-exp0.3

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

  8. Applied sum-log0.3

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

  9. Applied sum-log0.3

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

  10. Simplified0.3

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

  12. Applied exp-sum0.3

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

  13. Applied log-prod0.3

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

  14. Applied associate-+l+0.3

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

  15. Simplified0.3

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

  16. Final simplification0.3

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

Reproduce

herbie shell --seed 2019235 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :precision binary64
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))