Average Error: 0.4 → 0.0
Time: 9.6s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\log \left(\left(e^{d} \cdot e^{e}\right) \cdot \left(e^{b} \cdot \left(e^{a} \cdot e^{c}\right)\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\log \left(\left(e^{d} \cdot e^{e}\right) \cdot \left(e^{b} \cdot \left(e^{a} \cdot e^{c}\right)\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r2112043 = e;
        double r2112044 = d;
        double r2112045 = r2112043 + r2112044;
        double r2112046 = c;
        double r2112047 = r2112045 + r2112046;
        double r2112048 = b;
        double r2112049 = r2112047 + r2112048;
        double r2112050 = a;
        double r2112051 = r2112049 + r2112050;
        return r2112051;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r2112052 = d;
        double r2112053 = exp(r2112052);
        double r2112054 = e;
        double r2112055 = exp(r2112054);
        double r2112056 = r2112053 * r2112055;
        double r2112057 = b;
        double r2112058 = exp(r2112057);
        double r2112059 = a;
        double r2112060 = exp(r2112059);
        double r2112061 = c;
        double r2112062 = exp(r2112061);
        double r2112063 = r2112060 * r2112062;
        double r2112064 = r2112058 * r2112063;
        double r2112065 = r2112056 * r2112064;
        double r2112066 = log(r2112065);
        return r2112066;
}

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
Herbie0.0
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

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

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

  6. Applied add-log-exp0.3

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

  7. Applied add-log-exp0.3

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

  8. Applied add-log-exp0.3

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

  9. Applied sum-log0.3

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

  10. Applied sum-log0.3

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

  11. Applied sum-log0.1

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

  12. Simplified0.3

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

  14. Applied add-log-exp0.3

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

  15. Applied add-log-exp0.3

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

  16. Applied add-log-exp0.3

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

  17. Applied sum-log0.3

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

  18. Applied sum-log0.3

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

  19. Applied add-log-exp0.3

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

  20. Applied add-log-exp0.3

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

  21. Applied sum-log0.3

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

  22. Applied sum-log0.0

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

  23. Applied rem-exp-log0.0

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

  24. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

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

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