Average Error: 0.4 → 0.0
Time: 18.2s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\log \left(\left(e^{b} \cdot e^{e}\right) \cdot \left(e^{a} \cdot \left(e^{c} \cdot e^{d}\right)\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\log \left(\left(e^{b} \cdot e^{e}\right) \cdot \left(e^{a} \cdot \left(e^{c} \cdot e^{d}\right)\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r3487033 = e;
        double r3487034 = d;
        double r3487035 = r3487033 + r3487034;
        double r3487036 = c;
        double r3487037 = r3487035 + r3487036;
        double r3487038 = b;
        double r3487039 = r3487037 + r3487038;
        double r3487040 = a;
        double r3487041 = r3487039 + r3487040;
        return r3487041;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r3487042 = b;
        double r3487043 = exp(r3487042);
        double r3487044 = e;
        double r3487045 = exp(r3487044);
        double r3487046 = r3487043 * r3487045;
        double r3487047 = a;
        double r3487048 = exp(r3487047);
        double r3487049 = c;
        double r3487050 = exp(r3487049);
        double r3487051 = d;
        double r3487052 = exp(r3487051);
        double r3487053 = r3487050 * r3487052;
        double r3487054 = r3487048 * r3487053;
        double r3487055 = r3487046 * r3487054;
        double r3487056 = log(r3487055);
        return r3487056;
}

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

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

  5. Applied add-log-exp0.3

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

  6. Applied add-log-exp0.3

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

  7. Applied sum-log0.3

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

  8. Simplified0.3

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

  10. Applied add-log-exp0.3

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

  11. Applied add-log-exp0.3

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

  12. Applied add-log-exp0.3

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

  13. Applied sum-log0.3

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

  14. Applied sum-log0.2

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

  15. Applied add-log-exp0.2

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

  16. Applied add-log-exp0.2

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

  17. Applied sum-log0.2

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

  18. Applied sum-log0.0

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

  19. Applied rem-exp-log0.0

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

  20. Final simplification0.0

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

Reproduce

herbie shell --seed 2019151 
(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))