Average Error: 0.4 → 0.3
Time: 9.6s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[a + \log \left(\left(e^{e} \cdot e^{c}\right) \cdot e^{d + b}\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
a + \log \left(\left(e^{e} \cdot e^{c}\right) \cdot e^{d + b}\right)
double f(double a, double b, double c, double d, double e) {
        double r1949534 = e;
        double r1949535 = d;
        double r1949536 = r1949534 + r1949535;
        double r1949537 = c;
        double r1949538 = r1949536 + r1949537;
        double r1949539 = b;
        double r1949540 = r1949538 + r1949539;
        double r1949541 = a;
        double r1949542 = r1949540 + r1949541;
        return r1949542;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r1949543 = a;
        double r1949544 = e;
        double r1949545 = exp(r1949544);
        double r1949546 = c;
        double r1949547 = exp(r1949546);
        double r1949548 = r1949545 * r1949547;
        double r1949549 = d;
        double r1949550 = b;
        double r1949551 = r1949549 + r1949550;
        double r1949552 = exp(r1949551);
        double r1949553 = r1949548 * r1949552;
        double r1949554 = log(r1949553);
        double r1949555 = r1949543 + r1949554;
        return r1949555;
}

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 add-log-exp0.4

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

  4. Applied add-log-exp0.4

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

  5. Applied add-log-exp0.4

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

  6. Applied add-log-exp0.4

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

  7. Applied sum-log0.4

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

  8. Applied sum-log0.3

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

  9. Applied sum-log0.3

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

  10. Simplified0.3

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

  12. Applied add-log-exp0.3

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

  13. Applied add-log-exp0.3

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

  14. Applied add-log-exp0.3

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

  15. Applied sum-log0.3

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

  16. Applied sum-log0.3

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

  17. Applied rem-exp-log0.3

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

  18. Final simplification0.3

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

Reproduce

herbie shell --seed 2019156 
(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))