Average Error: 0.4 → 0.3
Time: 3.0s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + e^{\log \left(a + \left(b + c\right)\right)}\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + e^{\log \left(a + \left(b + c\right)\right)}\right)
double f(double a, double b, double c, double d, double e) {
        double r105455 = e;
        double r105456 = d;
        double r105457 = r105455 + r105456;
        double r105458 = c;
        double r105459 = r105457 + r105458;
        double r105460 = b;
        double r105461 = r105459 + r105460;
        double r105462 = a;
        double r105463 = r105461 + r105462;
        return r105463;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r105464 = e;
        double r105465 = d;
        double r105466 = a;
        double r105467 = b;
        double r105468 = c;
        double r105469 = r105467 + r105468;
        double r105470 = r105466 + r105469;
        double r105471 = log(r105470);
        double r105472 = exp(r105471);
        double r105473 = r105465 + r105472;
        double r105474 = r105464 + r105473;
        return r105474;
}

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 associate-+l+0.3

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

  5. Applied associate-+l+0.2

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

  6. Simplified0.2

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

  8. Applied associate-+l+0.2

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

  10. Applied add-exp-log0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2020035 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :precision binary64
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

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

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