Average Error: 0.4 → 0.2
Time: 12.2s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(c + d\right) + \left(a + b\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(\left(c + d\right) + \left(a + b\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r5128443 = e;
        double r5128444 = d;
        double r5128445 = r5128443 + r5128444;
        double r5128446 = c;
        double r5128447 = r5128445 + r5128446;
        double r5128448 = b;
        double r5128449 = r5128447 + r5128448;
        double r5128450 = a;
        double r5128451 = r5128449 + r5128450;
        return r5128451;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r5128452 = e;
        double r5128453 = c;
        double r5128454 = d;
        double r5128455 = r5128453 + r5128454;
        double r5128456 = a;
        double r5128457 = b;
        double r5128458 = r5128456 + r5128457;
        double r5128459 = r5128455 + r5128458;
        double r5128460 = r5128452 + r5128459;
        return r5128460;
}

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
Herbie0.2
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

Derivation

  1. Initial program 0.4

    \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]

  2. Taylor expanded around 0 0.4

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

  4. Applied associate-+l+0.3

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

  6. Applied associate-+l+0.2

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

  7. Final simplification0.2

    \[\leadsto e + \left(\left(c + d\right) + \left(a + b\right)\right)\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1.0 a 2.0 b 4.0 c 8.0 d 16.0 e 32.0)

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

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