Average Error: 0.4 → 0.0
Time: 20.2s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\log \left(\left(e^{c} \cdot e^{d}\right) \cdot \left(e^{a} \cdot \left(e^{e} \cdot e^{b}\right)\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\log \left(\left(e^{c} \cdot e^{d}\right) \cdot \left(e^{a} \cdot \left(e^{e} \cdot e^{b}\right)\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r4748972 = e;
        double r4748973 = d;
        double r4748974 = r4748972 + r4748973;
        double r4748975 = c;
        double r4748976 = r4748974 + r4748975;
        double r4748977 = b;
        double r4748978 = r4748976 + r4748977;
        double r4748979 = a;
        double r4748980 = r4748978 + r4748979;
        return r4748980;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r4748981 = c;
        double r4748982 = exp(r4748981);
        double r4748983 = d;
        double r4748984 = exp(r4748983);
        double r4748985 = r4748982 * r4748984;
        double r4748986 = a;
        double r4748987 = exp(r4748986);
        double r4748988 = e;
        double r4748989 = exp(r4748988);
        double r4748990 = b;
        double r4748991 = exp(r4748990);
        double r4748992 = r4748989 * r4748991;
        double r4748993 = r4748987 * r4748992;
        double r4748994 = r4748985 * r4748993;
        double r4748995 = log(r4748994);
        return r4748995;
}

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. Simplified0.3

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

  8. Applied add-log-exp0.3

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

  9. Applied add-log-exp0.3

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

  10. Applied sum-log0.3

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

  11. Applied add-log-exp0.3

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

  12. Applied add-log-exp0.3

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

  13. Applied add-log-exp0.3

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

  14. Applied sum-log0.3

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

  15. Applied sum-log0.2

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

  16. Applied sum-log0.0

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

  17. Applied rem-exp-log0.0

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

  18. Final simplification0.0

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

Reproduce

herbie shell --seed 2019129 +o rules:numerics
(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))