Average Error: 0.4 → 0.0
Time: 19.3s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\log \left(\left(e^{d} \cdot e^{a}\right) \cdot \left(e^{e} \cdot \left(e^{c} \cdot e^{b}\right)\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\log \left(\left(e^{d} \cdot e^{a}\right) \cdot \left(e^{e} \cdot \left(e^{c} \cdot e^{b}\right)\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r4816363 = e;
        double r4816364 = d;
        double r4816365 = r4816363 + r4816364;
        double r4816366 = c;
        double r4816367 = r4816365 + r4816366;
        double r4816368 = b;
        double r4816369 = r4816367 + r4816368;
        double r4816370 = a;
        double r4816371 = r4816369 + r4816370;
        return r4816371;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r4816372 = d;
        double r4816373 = exp(r4816372);
        double r4816374 = a;
        double r4816375 = exp(r4816374);
        double r4816376 = r4816373 * r4816375;
        double r4816377 = e;
        double r4816378 = exp(r4816377);
        double r4816379 = c;
        double r4816380 = exp(r4816379);
        double r4816381 = b;
        double r4816382 = exp(r4816381);
        double r4816383 = r4816380 * r4816382;
        double r4816384 = r4816378 * r4816383;
        double r4816385 = r4816376 * r4816384;
        double r4816386 = log(r4816385);
        return r4816386;
}

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 add-log-exp0.4

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

  4. Applied add-log-exp0.4

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

  5. Applied sum-log0.4

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

  6. Simplified0.2

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

  8. Applied add-log-exp0.2

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

  9. Applied add-log-exp0.2

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

  10. Applied add-log-exp0.2

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

  11. Applied sum-log0.2

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

  12. Applied sum-log0.2

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

  13. Applied add-log-exp0.2

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

  14. Applied add-log-exp0.2

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

  15. Applied sum-log0.2

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

  16. Applied sum-log0.0

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

  17. Applied rem-exp-log0.0

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

  18. Final simplification0.0

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

Reproduce

herbie shell --seed 2019133 
(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))